Assessment of Direct Shear Behavior in Normal and Ultra-High-Performance Concretes

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Title:
Assessment of Direct Shear Behavior in Normal and Ultra-High-Performance Concretes
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1 online resource (10 p.)
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english
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French, Robin E
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University of Florida
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Gainesville, Fla.
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Master's ( M.S.)
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University of Florida
Degree Disciplines:
Civil Engineering, Civil and Coastal Engineering
Committee Chair:
KRAUTHAMMER,THEODOR
Committee Co-Chair:
ASTARLIOGLU,SERDAR

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concrete -- impact -- push-off -- shear -- uhpc -- uhpfrc
Civil and Coastal Engineering -- Dissertations, Academic -- UF
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Civil Engineering thesis, M.S.
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Abstract:
Direct Shear is a sudden and catastrophic failure type commonly observed in reinforced concrete structures under highly impulsive dynamic loads, that can lead to sudden and catastrophic structural failure. The direct shear behavior of normal strength concrete (NSC) under both static and impact loading conditions is not well defined. Furthermore, new ultra-high performance concretes are being developed that have yet to be tested in direct shear. UHPC mixes entitled COR-TUF have been developed by the U.S. Army Engineer Research Center and Development Center (ERDC). One of the mixes developed contains steel fibers (COR-TUF1) and the other does not (COR-TUF2). As with any new material, it is important to fully characterize its properties. The purpose of the study presented in this paper was to conduct quasi-static and dynamic testing of both NSC and UHPC shear push-off specimens with varying reinforcement ratios. Preliminary results from testing were compared to the Hawkins shear transfer model to assess its suitability for predicting direct shear behavior of NSC and COR-TUF. The findings indicated that the model required modifications to adequately represent the behavior of NSC and COR-TUF specimens. Consequently, the model was modified with new coefficients for three types of concrete studied. This report presents the study, the findings and provides conclusions as well as recommendations for future research.
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by Robin E French.
Thesis:
Thesis (M.S.)--University of Florida, 2014.
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Adviser: KRAUTHAMMER,THEODOR.
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Co-adviser: ASTARLIOGLU,SERDAR.

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GeneralizedComponent-BasedModel forShearTabConnectionsS.D.Koduru1andR.G.Driver,M.ASCE2Abstract: Thebehaviorofaconventionalsteelsingle-plate(sheartab)connectionishighlydependentonthetypeofloadingtowhichitis subjected.Althoughtheseconnectionshavebeenstudiedprimarilyundershearloading,reflectingtheircommonusageingravityframing, theirbehaviorundercombinedloadingscenariosismorecomplex.Theobjectiveofthisstudyistodevelopandvalidateacomponent-based mechanicalsheartabconnectionmodelthataccountsfortheinteractionsofshear,axialload,andmoment.Thecomponent-based methodologyallowsforthedivisionoftheconnectionintoitsconstituentpartsandformodelingoftheforce-deformationrelationship ofeachpartseparately.Thus,theconnectionresponsetoabroadarrayofloadcombinationscanbeobtainedonthebasisofthegeometric andmaterialpropertiesoftheconnection.Themodelisvalidatedagainstexperimentalresultsfromavarietyofloadingregimes,andthe sensitivityofthemodelperformancetotheconnectionandmodelparametersispresented. DOI: 10.1061/(ASCE)ST.1943-541X.0000823 2013AmericanSocietyofCivilEngineers. Authorkeywords: Sheartabconnections;Component-basedmodel;Tension-shearinteraction;Sensitivityanalysis;Steelstructures; Progressivecollapse;Semi-rigidconnections;Numericalmodels;Analysisandcomputation.IntroductionProgressivecollapseiscommonlydefinedasthelossofstructural integritycausedbylocalizeddamagefromanextremeevent,in whichtheconsequentialstructuraldamageisdisproportionateto thecause.Inlightoftheuncertaintywithrespecttotheloading typeandmagnitude,notionalcolumnremovaliswidelyaccepted asanappropriateloadingcriterionforthedesignofbuildingsto preventprogressivecollapse[ Dept.ofDefense(DoD)2009 ; GSA2003 ].PertheDoDandGSAguidelines,thecolumnremoval isperformedinsuchawaythatitsconnectionstothesurrounding beamsareleftintact.Inthiscontext,thebeam-to-columnconnectionsplayasignificantroleinprovidingalternativeloadpaths followingthelossofacriticalload-supportingmember. Sheartabbeam-to-columnconnectionsarecommoninsteelframedstructuresandareoftendesignedsolelyfortransferring thegravityloads,primarilyindirectshear.Thisconnectionconsists ofaverticalsteelplateweldedtoacolumnorgirderweborflange andboltedtothesupportedbeamweb.Fig. 1 depictsatypicalshear tabanddefinesthesymbolsusedinthispaperfortheassociated geometricparameters.Inthecolumn-removalscenario,these connectionsaresubjectedtoacombinationoftensileforcesand largerotations,attributedtothecatenaryactionthatdevelopsin thebeams,inadditiontoshearandmoment.Hence,theresponse oftheconnectiontotheseatypicalloadcombinationsgainscritical significanceforaccuratelyassessingtheprogressivecollapse resistanceofsteelstructures. Numericalmodelsforthedeterminationofconnectionresponse usuallyuseeitherhigh-fidelityfinite-elementmethodsorspringbasedmechanicalmodels.Althoughfinite-elementmodelscan beinformativeintheabsenceofexperimentalstudies,theyrequire considerableefforttomodelthecontactbehaviorbetweenthebolts andtheplateorbeamwebaccurately.Furthermore,thecomputationalcostsassociatedwiththeanalysisrenderthemimpracticalfor applicationsofwhole-buildinganalysisbecauseofthelargenumberofconnectionsinvolved.Hence,thereisasignificantinterestin thedevelopmentofappropriatesimplifiedmechanicalmodels. Insimplespring-basedmechanicalmodels,theoverallresponse oftheconnectionforeachloadingtype(e.g.,moment,shear, tension)ischaracterizedbyasinglelinearornonlinearforce – deformationspring.Theeffectofloadcombinationsontheconnectionisaccountedforbytheexplicitformulationoftheinteraction betweenthespringresponses.However,thedevelopmentofappropriateinteractionrelationshipsrequiresalargeexperimental datasettoaccountforthevariabilityarisingfromdifferingload combinationsandconnectionparameters. Component-basedmodelingisanextensionofthesimplespring model,inwhichasingle-connectionspringisreplacedbya compositeof “ componentsprings. ” Eachcomponentspring definestheforce-deformationrelationshipofaparticularconnectioncomponent.Thisfacilitatestheuseofexistingdataoneachof theconnectioncomponentsandpermitsthedeterminationof connectionresponseoverawiderangeofparameters.Inthis approach,theseriesandparallelarrangementofthecomponent springsaccountsfortheinteractionoftheshear,axial,andmoment forcesandeliminatestheneedforexplicitinteractionformulation intheindividualspringresponsedefinitions.LiteratureReviewAccordingtopreviousexperimentalstudies,afewcomponentbasedconnectionmodelshavebeenproposedforuseinprogressive1PostdoctoralFellow,Dept.ofCivilandEnvironmentalEngineering, Markin/CNRLNaturalResourcesEngineeringFacility,Univ.ofAlberta, Edmonton,AB,CanadaT6G2W2(correspondingauthor).E-mail:smitha@ ualberta.ca 2Professor,Dept.ofCivilandEnvironmentalEngineering,Markin/ CNRLNaturalResourcesEngineeringFacility,Univ.ofAlberta, Edmonton,AB,CanadaT6G2W2.E-mail:rdriver@ualberta.ca Note.ThismanuscriptwassubmittedonAugust15,2012;approvedon February12,2013;publishedonlineonFebruary14,2013.Discussion periodopenuntilFebruary28,2014;separatediscussionsmustbesubmittedforindividualpapers.Thispaperispartofthe Journalof StructuralEngineering ,ASCE,ISSN0733-9445/04013041(10)/ $25.00.ASCE04013041-1J.Struct.Eng.

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collapseassessments.InthemodelbySadeketal.( 2008 ),anumber ofnonlineartranslationalsprings,equaltothenumberofbolts, arearrangedinparalleltoaccountfortheaxial-momentforce interaction.Thespringcapacitiesaredeterminedonthebasisof thecapacityofthegoverningconnectionfailuremodeunderaxial loadalone.Thestiffnessandthedeformationatfailureforeach springaredefinedonthebasisoftherecommendationsof FEMA Report355D ( FEMA2000 ).Themodelconsiderstheshearbehavioroftheconnectiontoberigidandhencedoesnotaccountforits shearcapacityorverticaldeformation.Themodelwasvalidated againstthephysicaltestsofLiuandAstaneh-Asl( 2004 )on connectionstobeamsoverlainbyaconcreteslabunderapplied shearandmoment.ArecentextensionofthismodelbyMain andSadek( 2012 )includestheshearandaxialinteractionbased ontheshearandaxialdeformationatfailurefortheboltshear andboltbearingfailuremodes.Thismodelisvalidatedagainst theexperimentalresultsofThompson( 2009 )andshowsavariation of 1 8 to 26 1% errorinthemodelpredictions. TaibandBurgess( 2011 )proposedacomponent-basedmodel fromthefinite-elementanalysesofSarrajetal.( 2007 )andtests conductedbyYuetal.( 2009 ).Althoughthefocusoftheresearch programwasonsheartabconnectionbehaviorinfireconditions, elevatedtemperatureisnotarequirementofthemodelitself.This modelusesdistincttranslationalspringsforbearingbehaviorofthe connectingplateandbeamwebincompressionandtensionand shearbehaviorofthebolt.Thesespringsareconnectedinseries torepresentalapjointatagivenbolt.Suchlap-jointcomposite springs,placedtocorrespondwitheachboltlocation,actinparallel toaccountfortheaxial-momentloadinteractionontheoverallconnection.Theshearbehavioroftheconnectionisrepresentedbya singletranslationalspringperpendiculartoallthelap-jointsprings. Althoughthismodelconsidersshearbehaviorexplicitly,anyinteractionbetweentheshearandaxialstresseswithintheconnecting plateisneglected.ThemodelwascalibratedtothetestresultsofYu etal.( 2009 ). YimandKrauthammer( 2012 )proposedacomponent-based modelforsheartabconnectionsundermonotonic,cyclic,or high-speedloadsarisingfromdefinedhazardsrepresenting progressivecollapse,earthquake,andblastconditions.Thismodel useseightdifferentcomponentspringstorepresentcolumnweb shear,boltshear,andthelap-jointbehaviorbetweentheplate andbeamwebunderaxialloads.Asthismodelisfocusedon characterizingthemoment-rotationresponseundermonotonic andcyclicloads,itwasvalidatedagainstcyclicloadtestscarried outbyCrockerandChambers( 2004 )onconnectionsunderapplied momentsonly.Thus,thismodelmaynotbeappropriateforusein progressivecollapseassessmentsinwhichaxialforceandshear becomedominant. Mostspringmodelsavailableintheliteratureforprogressive collapseassessmentsdonotconsidertheinteractionsamongshear, axialload,andmoment.Thesemodelsconsidertheshearresponse tobeeitherrigidorindependentoftheaxial-momentresponseof theconnection.Furthermore,mosttestsusedforvalidationdonot includethetypeofloadcombinationsexpectedunderthecolumnremovalscenario;assuch,testdatahavebeenrelativelyscarce untilrecently.Inthepresentstudy,acomprehensivemodelthataccountsforshear-axial-momentloadinteractionsisdeveloped. Althoughtheprimarypurposeofthedevelopmentofthemodel isforapplicationtoprogressivecollapseassessments,itisvalidated againstawiderangeofloadcombinationsbyusing11test cases(loadtypes)from6differentexperimentalprograms(total of26individualconnectiontests).Ofthese11cases,6were representativeofcatenaryactioninthecolumn-removalscenario (17individualconnectiontests).ProposedModelIntheproposedmodel,thesheartabconnectionisrepresentedbya groupof “ boltsprings, ” whichareeachacompositeofseveral componentsprings,asshowninFig. 2 .Theboltsprings,equal innumbertothenumberofboltsintheconnection,arearranged toactinparallelandaccountfortheinteractionofaxialforceand moment.Inturn,eachboltspringrepresentsagroupoftranslational springsarrangedinseriesandparallelthataccountforthebehavior ofeachconnectioncomponentandtheinteractionofshearandaxialforces.Thecomponentsprings,depictedsymbolicallyinFig. 2 representwelddeformation,plateyieldingintension(horizontal) andshear(vertical),boltshear,platefractureintension(horizontal) andshear(vertical),andedgetear-outoftheplateandtheconnectingbeamwebcausebyboltbearing.Theshearandaxial-load capacitiesareconsideredseparatelyfortheplateyieldingandplate fracturecomponents,andanellipticalinteractionisexplicitly imposedontheloadcapacities.Fortherestofthebolt-spring components(i.e.,weld,boltshear,plateedgetear-outandwebedge LevsbsbLpW p Thickness, tp LevLeh Wt Fig.1. Typicalsheartabandgeometricparameters Fig.2. Component-basedmodelofsheartabconnectionASCE04013041-2J.Struct.Eng.

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tear-out),thecombinedloadfromtheshearandaxialforcesis consideredtoactdirectlyintheresultantforcedirection,and thecomponentcapacityiscomputedaccordingly. Themonotonicforce-deformationrelationshipforeachcomponentspringisderivedfromtheliterature.Theweldcomponentis modeledaccordingtotherelationshipdevelopedbyLesikand Kennedy( 1988 )forfilletwelds.Thespringmodelsfortheplate yieldingintensionandsheararebilinear,withaninitialstiffness andyieldstrengthcomputedaccordingtotheplategrosscrosssectionalpropertiesandthewidthoftheplatebetweentheweld toeandtheinneredgeoftheboltholeandassumingfixityalong theweldtoe.Theyieldstrengthdemarcatesthetransitionpointto theplasticbehaviorwitha2%hardeningratio.Theboltshear force – deformationrelationshipisbasedonthemodelbyYuetal. ( 2009 ),withtheempiricalparametersderivedfromdatareported byMooreetal.( 2008 ),andisrepresentedas bs F Kbs Kb 1 F Fbs6 1 where bs= boltshearcomponentdeformation; F = resultantshear forceinthebolt; Fbs= boltshearcapacity,computedastheproduct ofthebolttensilecapacity, Cb 1(conversionfactorfromtensileto shearcapacity),and Cb 2(conversionfactorforeffectivecrosssectionalarea); Kbs= initialboltshearstiffness,computedas Kbs Kb 2G Ab eff = db(where G isshearmodulus; Ab effiseffectiveboltcross-sectionalarea;and dbisboltdiameter);and Kb 1and Kb 2= empiricalfactorscontrollingthepostyieldandinitial stiffnesses,respectively.Theplatefractureintensionandshear aremodeledasrigidspringswithfinitestrength,reflectingthe smallcontributionofthismodetotheoveralldeformationresponse oftheconnection.Therupturestrengthsofthecomponentsin tensionandsheararecomputedatthenetplatesectionatthecenter oftheboltline.Theforce-deformationrelationshipsfortheedge tear-outcomponentsfortheplateandthebeamwebarebased onthemodelbyRexandEasterling( 2003 ).Itisrepresentedas F Ke 1 Ki et 1 Ki et= FetMp 2 Ke 2 Ki et 2 where F = resultantforceontheedgetear-outcomponent; et= deformationofthiscomponent; FetM= edgetear-outcapacity, computedas FetM Ce 1futLe(where Ce 1isanempiricalfactor toconvertthematerialtensilecapacitytotheshearcapacityand accountforthefactthatfailureoccursontwoparallelshearplanes adjacenttothebolt; fuisthematerialtensilecapacity; t isthe materialthickness;and Leistheedgedistanceinthedirection oftheresultantforce); Ke 1and Ke 2= empiricalfactorscontrolling stiffness;and Ki= effectivestiffness,computedas Ki K 1 br K 1 b K 1 v 1,where Kbr Ke 3tfy db= 25 4 0 8. Ke 3isanempiricalcalibrationfactor; fyistheyieldcapacity; and Kband Kvarethebendingandshearstiffnessesoftheportion oftheplateorbeamwebbetweentheboltholeandthefreeedge, respectively.Detailsontheexplicitformulationsandempirical factorsconsideredarereportedbyKoduruandDriver( 2012 ). Inadditiontothespringbehaviorsdescribedpreviously,the componentmodelsaccountforthefollowingphysicalphenomena: (1)unloadingbehavioroftheboltspringsalongapaththatis potentiallydifferentfromthatusedforloading;(2)component springresponsesintensionandcompression;(3)capacitydegradationfollowingthepeakload;and(4)boltslip.Underthe monotonicapplicationtoaconnectionofbothmomentandaxial tension,theunloadingofanindividualboltspringfromaninitial compressionoccurswhentherateofapplicationofthetensile springforceexceedsthatofthecompressionbecauseofthe connectionrotation.Thisunloadingsignalstheinitiationofthe catenaryresponseoftheconnection.Whentheforceinthebolt springonreversalislessthan50%ofitspeakcompressivecapacity, theunloadingisconsideredtooccurwithoutanyresidualdeformation.Theunloadingstiffnessinthiscaseisbasedontheboltspring forceanddeformationatthestartofunloading.Astheboltspring behaviorishighlynonlinear,residualdeformationsareexpectedto occurafterloadshigherthan50%ofthepeakcapacity.Inthiscase, theunloadingoccurswiththestiffnessequaltotheinitialbolt springstiffnessuntiltheforcereducestozero.Theunloadingstiffnessthenbecomeszerountilthenetdeformationalsoreacheszero. This “ pinching ” effectintheresponseistoaccountforthesliding oftheboltfromoneendoftheelongatedboltholetotheother duringtheloadreversal.Itisbasedontheassumptionthatthe plasticdeformationoftheboltspringisprimarilycausedbythe elongationoftheboltholeunderboltbearing.Thus,foratypical connection,allplasticdeformationincompressionatloadshigher than50%ofthepeakboltspringcapacityismodeledtobe concentratedinthecomponentspringwiththelowesttangential stiffness.Fig. 3 showstheconceptualunloadingbehaviorofthe boltsprings. Duringthecompressionphase,theboltbearsawayfromthe plateedge;thus,thefailuremodeofaboltspringcannotbemodeledonthebasisofedgetear-outoftheplateorbeamweb.Instead, failureoccursbecauseofcrushingoftheplatesurroundingthebolt hole.Thus,themaximumcapacityoftheso-callededgetear-out componentspringdiffersincompressionandtension,asthefailure modeincompressioniscausedbyboltbearing,whereasintension itiscausedbyedgetear-out.Inthemodel,thecapacityofthe componentspringincompressionisincreasedbytheratioofthrice theboltdiameter( db)tothehorizontaledgedistance( Leh)to representtheupperlimitoftheboltbearingcapacityincompression( KoduruandDriver2012 ).Allothercomponentspringsare modeledtohaveidenticalbehaviorintensionandcompression. Theedgetear-outcomponentspringsalsoexhibitaductile failurewithagradualdegradationafterreachingthepeakcapacity intension.However,experimentaldataaresparsefordevelopinga parameterizedmodeldefiningthedeformationatthefailureinitiationandthedegradationstiffnessthataccountsfortheeffectsof platethickness,tensilecapacity,boltdiameter,andboltholesize. OnthebasisofexperimentaldatabyKimandYura( 1999 )and 0 0 Unloading from > 50% capacity Unloading from < 50% capacity Degradation for edge tear-out failure Load loss after brittle failure Displacement KdegForce Tension Compression Fig.3. BoltspringunloadinganddegradationbehaviorsASCE04013041-3J.Struct.Eng.

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MozeandBeg( 2010 )andcomponentmodelingofTaiband Burgess( 2011 ),thedeformationoftheboltspringatthefailure initiationisconsideredtobe Leh= 2 ,whereastheloadcapacity isassumedtobecompletelyexhaustedatadeformationnogreater than Leh,followingalinearstrengthdegradationpath.Accordingto theseassumptions,thedegradationstiffnessoftheedgetear-out componentspringiscomputedas Kdeg FetMLeh Cstiff 0 5 3 where Kdeg= degradationstiffness; FetM= maximumcapacityof theedgetear-outcomponent;and Cstiff= empiricalfactorto accountfortheuncertaintyinthedegradationstiffness.Theupper boundof Cstiffis1.0accordingtothepreviousrationale,whereas thelowerboundisconsideredtobe0.5,whichimpliesafull capacitylossimmediatelyfollowingthefailureinitiation.For theremainderofthenonductilefailuremodes — weldrupture,bolt shearfailure,andplatenet-sectionfracture — theloadlossis modeledasbrittleandabrupt.Fig. 3 showsthedegradation behavioroftheboltspringonfailureoftheedgetear-out componentincontrasttothebrittlefailuremode. Boltslipformsacriticalfactorinincreasingthesheartab connectionductility.Itoccurswhentheappliedaxialloadon theconnectionexceedsthefrictionalresistanceofferedbythebolt installationmethodandmatingsurfaceroughnesses.Thiseffectis noticeableinphysicaltests,inwhichtheconnectionstiffnessdrops significantlyafterthefirstfewloadsteps( Yuetal.2009 ; Oosterhof andDriver2012 ; Weigandetal.2012 ).Althoughinitialresistance toboltslipdependsontheboltingmethod,thefrictionalresistance causedbyanyboltingmethodislowerthantheconnection capacity.Thiscausestheboltslipalwaystooccurlongbefore theconnectionfails;thus,theinitialfrictionalresistancedoes notinfluencetheultimateconnectioncapacity( Crockerand Chambers2004 ).Therefore,thefrictionalresistanceinthe proposedmodelisnotmodeledexplicitly;however,theincreased connectionrotationalductilitycausedbyboltslipisaccountedfor byconsideringaninitialdeformationallag — equivalenttoone-half ofthedifferencebetweentheboltholediameter( dh)andthebolt diameter( db) — ineachedgetear-outcomponentofaboltspring (sheartabandbeamweb),beforetheaccumulationofaxialforce. Theeffectofboltslipisconsideredonlyforconnectionsthatdonot havesignificantshearloadappliedbeforetheapplicationof rotationandaxialloadsbecausethepresenceofsheartendsto eliminatetheoccurrenceofdiscreteslippageevents.ModelValidationThemodelvalidationisperformedundermonotonicloading conditions.Althoughtheconnectionsareexpectedtoexperience cyclicloadingcausedbythesuddencolumnremoval,the maximumrotationandcapacitydemandsontheconnectionoccur withinthefirsthalf-cycleoffreevibrationofthestructure.Followingthisrationale,theDoD( 2009 )andGSA( 2003 )guidelinesalso recommendadynamicanalysisuptothefirstpeakload.In addition,theproposedmodelisolatestheconnectionbehaviorfrom thesurroundingstructuralelementsandthereforeneglectssuch aspectsastheinfluenceofthefloorslab,potentialbearingof thebeamflangeonthesupportingcolumn,andthecolumnweb shear.Assuch,thesefeaturesarenotconsideredinthevalidations (thetestsusedtoconductthevalidationsalsoexcludethem), althoughthemodelcouldbeextendedtoincludetheseeffectswith additionaltranslationalspringscharacterizingthesebehaviors. Full-scalesheartabconnectionswithavarietyofgeometric parametersandsubjectedtoanarrayofloadcombinationsare consideredinthemodelvalidationprocess.Theloadcombinations includemomentonly( Crocker2001 ; CrockerandChambers 2004 ),combinationsofshearandtensileloadingwithafixed rotation( Guravich2002 ; GuravichandDawe2006 ),combinations ofshearandmoment( Astanehetal.1989 ),andcatenaryaction underavarietyofgeometricscenarios( Thompson2009 ; Oosterhof andDriver2012 ; Weigandetal.2012 ).Theselectionofthesetests isbasedprimarilyontheavailabilityofbothdetailedinformation aboutthetestspecimenandsufficientresultstoenabletheisolation ofconnectionbehaviorfromthetestsubassembly. Tables 1 and 2 showthenominalvaluesformaterialand geometricparametersofthetestspecimens.Forthepurposeof modelvalidation,materialparametersobtainedfromcoupontests andas-builtmeasurementsofthegeometricparametersareused wherereported.Forthetestspecimenswithonlythenominal valuesavailable,thesevaluesareconvertedtomeanvaluesbyusing themultiplicativebiasfactorspresentedinTable 3 Forthetestsinwhichtherequiredmodelinputisnotreported, thenumericalvaluesareestimatedasdescribedinthefollowingto maintainconsistencyinthemodelinputparameters.ForTestcase 3,themodelinputforappliedshearloadismeasuredas237kN, equaltotheaverageofthethreetestloads — approximatelyequalto thenominaldesignshearcapacity — appliedtothreenominally identicalsheartabconnectionsbyGuravich( 2002 ).ForTestcases 4and5,thebeamwebthicknessesareestimatedas14.3and 15.3mm,respectively,accordingtothebeamlength-to-depthratios andplasticmomentcapacitiesreportedbyAstanehetal.( 1989 ). Table1. LoadingTypesandMaterialPropertiesforTestsUsedinModelValidation Testcase Primary loading type Numberof nominally identical specimens Weldstrength, Xu(MPa) Boltstrength, fub(MPa) Yield strength(MPa) Tensile strength(MPa) Reference Plate, fypWeb, fywPlate, fupWeb, fuw1Moment1485830a248345350450Crocker( 2001 ) 2Tension3485830300350450450Guravich( 2002 ) 3Shear+tension3485830300345450450Guravich( 2002 ) 4Shear+moment1485830a248248400350Astanehetal.( 1989 ) 5Shear+moment14851,040a248345400450Astanehetal.( 1989 ) 6Catenary4485830248345400450Thompson( 2009 ) 7Catenary6485830248345400450Thompson( 2009 ) 8Catenary4485830248345400450Thompson( 2009 ) 9Catenary1485830248345400450Weigandetal.( 2012 ) 10Catenary1485830248345400450Weigandetal.( 2012 ) 11Catenary1485830300350450450OosterhofandDriver( 2012 )aThreadsincludedinshearplane.ASCE04013041-4J.Struct.Eng.

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Furthermore,tofacilitateconsistentcomparisonsofthemodel resultswiththetestdata,twoadditionalaccommodationswere made:(1)forTestcases6and8,thespecimenswithreported measurementdiscrepancyorunintendedloadpaths( Thompson 2009 )aredisregarded;and(2)forTestcases9and10,theconnectioncapacities — reportedasaratioofthemeasuredvaluetothe designshearcapacity — aredeterminedbyconsideringthedesign shearvaluestobe256and348kN,respectively( Weigand etal.2012 ). Theconnectionanalysisisperformedbydisplacement-based loadcontrolconformingtotheexperimentalloadingprotocol. Ateachloadstep,aboltspringissubjectedtohorizontal elongation,whichincludeselongationcausedbyaxialtension androtation,inadditiontotheappliedshear.Throughaniterative process,theaxialforceintheboltspringiscomputedsuchthatthe horizontalcomponentofthetotaldeformationisequaltothe appliedelongation.Duringtheiterativeprocess,allcomponents ofaboltspringaresubjectedtotheresultantoftheappliedshear andtrialaxialforces.Inthecasesoftheplateyieldingandplate fracturecomponents,theresultantforceisresolvedintohorizontal andverticalcomponentsthatareappliedtotheassociatedaxialand shearsprings,respectively. Fortestcasesthatarepartofatwo-spansubassemblyunder simulatedcolumnloss,theappropriaterotations,elongations, andshearforcestobeappliedarecomputedaccordingtothe three-hingedbeammodelbyOosterhofandDriver( 2011 ). Therefore,foreachunitofrotation( )appliedtotheconnection, thecorrespondingconnectionelongationis 0 5 L 1 cos 1 4 where = axialelongationappliedtotheconnection;and L = prototypebeamlengthbetweentheconnectionsinthetestcase [forTestcases6 – 8, L 1,896 mm( Thompson2009 );forTest cases9and10, L 14,630 mm( Weigandetal.2012 );andfor Testcase11, L 8,000 mm( OosterhofandDriver2012 )]. However,inthecaseofrotationallyflexibleconnections,for example,withthreeboltsorfewer,therelationshipinEq.( 4 ) maynotholdbecauseofthepossibilityofnear-simultaneousslip oftwobolts,causingasmallrotationwithoutthedevelopmentof anysignificantaxialforce.Therefore,theconnectionelongation willbelowerthanthatpredictedbyEq.( 4 ),asfollows: 0 5 L 1 cos s 1 5 where s= rotationcausedbyboltslipineachconnectionandis approximatedas s 1 2 L 2 1 s 6 where dh db ,whichcharacterizestherelativemovementof thecenteroftheboltholeinthebeamwebtothecenterofthebolt holeintheplate.Here,thediametersofboltholesinthebeamweb andtheplateareassumedtobeequal,andboththeboltholesare assumedtobecenteredwiththeboltbeforetheslipoccurs.Forthis loadingregime,theinitiallagisnotaddedtotheindividualbolt springs.Inthetestsinwhichelongationisdirectlyappliedto theconnection,itiscomputedaccordingtoEq.( 4 )byusingthe beamendrotationmeasurements.Fortestsofrotationallyflexible connections,theconnectionrotationislowerthanthebeamend rotation,withthedifferenceequalto s. Eqs.( 4 )and( 5 )aredevelopedforbeamswithasheartab connectionateachendandwiththeassumptionthatthetotal elongationrequiredbybeamrotationissharedequallybetween thetwoconnections.InthetestsbyThompson( 2009 ),thetest beamhadasheartabconnectionatoneendandatruepinconnectionattheother.Hence,intheanalysisofTestcases6 – 8,theaxial elongationappliedtotheconnectionisassumedas 2 ,and sis computedbysubstituting 2 dh db inEq.( 6 ).Furthermore, thetestsetupconsistedofapplyingverticaldisplacementstoa columnstubconnectedtoatestbeamoneachside.Inthemodel validation,whichconsidersonlythesheartabconnectionbehavior isolatedfromthissubassembly,theappliedloadisassumedtobe symmetricallydistributedbetweenthetwoconnections. Thevalidationoftheproposedmodelisperformedbycomparingpeakcapacitiesandthecorrespondingdeformations.Fortest caseswithmultiplespecimens(Testcases2,3,6,7,and8),the modelpredictionsarecomparedwiththeaveragetestresultsof nominallyidenticalconnections.Fig. 4 comparesatypicalmodel Table2. GeometricPropertiesforTestsUsedinModelValidation Test caseaNumber ofbolts, nbdb(mm) dh(mm) Wt(mm) sb(mm) Platedimensions, Lp Wp tp(mm) Webthickness, tw(mm) Leh(mm) Lev(mm) 161920.58.076 457 108 10 12.038.038.0 231920.58.080 230 100 7 9 27.835.035.0 331920.58.080 230 100 7 9 27.835.035.0 431921.06.276 229 108 9 5 14.338.138.1 551921.05.676 362 98 9 5 15.328.628.6 631920.56.476 229 127 9 5 17.138.138.1 741920.56.476 305 127 9 5 17.138.138.1 851920.56.476 381 127 9 5 17.138.138.1 931920.56.476 229 114 9 5 7.638.138.1 1041920.56.476 305 114 9 5 7.638.138.1 1151921.08.080 390 110 6 4 14.035.035.0aThereferenceforeachtestcaseisshowninTable 1 Table3. MaterialandGeometricPropertyDistributionParameters(Data from KoduruandDriver2012 ) ParameterBiasfactorCoefficientofvariationDistribution Xu1.1270.082Lognormal fyp1.110.054Lognormal fup1.190.034Lognormal fyw1.090.054Lognormal fuw1.120.046Lognormal fub1.180.045Lognormal Wt1.070.154Lognormal tp1.040.025Lognormal tw1.040.025LognormalASCE04013041-5J.Struct.Eng.

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predictionwiththeassociatedtestdata.Ingeneral,themodel performswellinpredictingthemoment,shear,andtensile responsesoftheconnection,includingatlargerotationswhere significantconnectiondeteriorationhasaccumulated.Although slightlyunderpredictingthepeakvaluesofmomentandtension, thepeakshear — representativeoftheload-carryingcapacityof thesystem — ispredictedaccurately.Afterthepeakloadintension, themodelpredictsasomewhatmoregradualaxial-loadlossinthe boltspringsthanwasobservedintheexperiments,buttheoverall trendofthedescendingbranchisreasonable. Table 4 showsthereportedexperimentalresultsandmodel predictionsforthepeakmoment,shear,andtensionachievedin eachcase,andTable 5 showsrotationsatthepeakmomentand tensionandtheaxialelongationatfailure.Fig. 5 comparespercentageerrorsinthemodelpredictionswiththemeanexperimental resultsbasedonTable 4 .Apositivedifferenceindicatesanoverprediction,andanegativedifferenceindicatesanunderprediction ofthemodelcomparedwiththeassociatedexperimentalresult.For thetestcaseswithmultiplespecimens,thepercentagedifferenceof eachindividualtestresultfromthemeanvalueisalsopresented (symbols)toindicatethetotalvariationofthetestdata.Similarly, Fig. 6 showsthepercentageerrorinmodelpredictionsforthedeformationsacrossallthetestcasesconsideredbasedonTable 5 .For thetestswithmultiplespecimens,thepercentagedifferenceofan individualtestresultfromthemeanvalueisalsoshowninFig. 6 Tables 4 and 5 andFigs. 5 and 6 showthatthemajorityofthe modelpredictionsarewithin10%oftheexperimentalresults.The modelperformedwellinpredictingpeakforcesandthedeformationforsingle-loadcases,asseenintheresultsforthemoment-only loadingcase(Testcase1)andthetension-onlyloadingcase(Test case2).Inthepresenceofsignificantshear,themodelperformed reasonablywellinpredictingthemaximumforcesandrotations (Testcases3 – 5).Furthermore,byexplicitlymodelingtheeffect ofshearandtensioninteraction,themodelpredictsalowertensile capacityforTestcase3thanTestcase2thatisclosetothetest result,eventhoughthetwoconnectionsarenominallyidentical. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 100 200 300 400 500 Rotation (rad)Force (kN) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 10 20 30 40 50 60 Moment (kN.m) Moment data Moment model Tension data Tension model Shear data Shear model Moment Tension Shear Fig.4. ComparisonofthemodelpredictiontothetestdataofOosterhofandDriver( 2012 )forafive-boltconnection Table4. ComparisonofPeakTestForceswithModelPredictions TestcaseaMoment (kNm)Shear(kN)Tension(kN) TestModelTestModelTestModel 192.583.0 ———— 2 ———— 373b371 3 ———— 305b327 431.528.2418368 —— 571.262.9578534 —— 618.5b23.429b33203b236 736.5b37.038b39211b302 866.4b68.249b45234b232 9 —— 3940492475 10 —— 6969638593 1151.046.07574460413aThereferenceforeachtestcaseisshowninTable 1 .bAverageofallnominallyidenticaltests. Table5. ComparisonofTestDeformationswithModelPredictions Test caseaRotation(rad) atmaximum Displacement (mm) MomentTension Axial elongation TestModelTestModelTestModel 10.0360.039 ———— 2 ———— 19b18.5 3 ———— 15b11.8 40.0560.058 ———— 50.0530.050 ———— 60.086b0.0880.132b0.113 —— 70.069b0.0640.104b0.114 —— 80.067b0.0630.094b0.104 —— 9 —— 0.0660.065 —— 10 —— 0.0720.078 —— 110.040.0410.080.077 ——aThereferenceforeachtestcaseisshowninTable 1 .bAverageofallnominallyidenticaltests.ASCE04013041-6J.Struct.Eng.

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Theproposedmodelunderpredictstheaxialelongationwhen failureoftheplatefracturecomponentoccurs,asseeninTable 5 forTestcase3.However,thetestdataitselfforaxialelongationin Testcase3hasalargevariability,asseeninFig. 6 ,indicatingthat theseresultsmaybesensitivetotheappliedshearorinfluencedby apotentialinteractionbetweenplatefractureandplateedgetear-out failuremodes. Forthecaseswithcatenaryaction,themodelperformed reasonablywellinpredictingthepeakforcesanddeformationsfor four-andfive-boltconnections(i.e.,Testcases7,8,10,and11). Theobservedpredictionerrorsarepartiallyaccountedforbythe variationofthetestdataitself,asseeninFig. 5 forTestcase7. Theunderlyingphenomenonforthislargevariationisdiscussed inthefollowingsection.Forthethree-boltconnectionsunder catenaryaction(Testcases6and9),theinclusionoftheboltslip effectaccordingtoEq.( 5 )improvedthemodelperformance significantly.However,Figs. 5 and 6 showthatthemodel predictionsforTestcase6havemorethan10%errorassociated withthepeakforcesandtherotationatthepeaktension,whereas Testcase9hasnegligibleerrorinbothpeakforcesandrotation predictions.Fig. 7 showsthethree-boltconnectionresponseswith andwithoutboltslipconsiderationforTestcase6,whichare comparedtotheexperimentalresultsofThompson( 2009 )fora three-boltconnectionwiththeboltshearfailuremode.Itisevident thattheinclusionoftheboltslipsignificantlyreducestheerrorin thepredictionofpeaktensionbutincreasestheerrorinthepredictionoftheconnectionrotationatfailure.Thefactorsinfluencing theseerrorsarediscussedsubsequently.SensitivityAnalysisManyaspectscontributetotheabilityofacomponentmodelto capturetheoverallphysicalresponsesofaconnection,buttheaccuraciesofthevariousinputparametersarenotnecessarilyofequal importanceinpredictingthekeyresponseparameters.Toassessthe relativeimportanceofthematerialandgeometricpropertiesandthe modelparameters,asensitivityanalysisisperformedforthe catenaryloadcases(Testcases6 – 11)becausetheyincludeall oftheforcedemandcomponentsapplicabletoageneralizedmodel: shear,axial,andmoment.AglobalsensitivityanalysiswithMonte Carlosamplingisperformedbyusingallparametersasuncorrelatedrandomvariables.Table 6 showsthedistributionsofmodel parametersinfluencingtheboltshearandedgetear-outcomponents thatareusedinthesampling( KoduruandDriver2012 )inaddition tothematerialandgeometricpropertieslistedinTable 3 .Model parametersinfluencingtheweldcomponent,alongwiththerest ofthematerialandgeometricproperties,arenotconsideredfor thesensitivityanalysisastheyhavelessthan2%coefficientof variation( KoduruandDriver2012 ).Fromthesamplingresults, thesensitivityofapeakforceparametertotheinputrandom variablesiscomputedaccordingtoalinearregression,andthefirst fourmostinfluentialvariablesarelistedinTable 7 .Thevariables correspondingtotheboltshearstrength( Cb 1, fub)andedge tear-out( Ce 1)tendtobethemostinfluentialforthepeaktension andshear,whereasacombinationofstrength-andstiffness-related variablesfortheboltshear( Cb 1, fub, Kb 2)andedgetear-outcomponent( Ce 1, Ke 1, Ke 3)arethemostinfluentialforthepeakmoment formostofthetestcases.InTestcase11,asthefailuremodeis 1 2 3 4 5 6 7 8 9 10 11 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 Test case% Difference from mean test value Moment test result variation Shear test results variation Tension test results variation Moment model error Shear model error Tension model error Fig.5. Peakconnectionforce;modelpredictionerrorsanddeviationof individualtestresultsfrommeantestvalues 1 2 3 4 5 6 7 8 9 10 11 -50 -40 -30 -20 -10 0 10 20 30 40 50 Test case% Difference from mean test value Elongation test results variation Moment rotation test results variation Tension rotation test results variation Elongation model error Moment rotation model error Tension rotation model error Fig.6. Connectionelongationandrotationatmaximummomentand tension;modelpredictionerrorsanddeviationofindividualtestresults frommeantestvalues 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 50 100 150 200 250 300 350 Rotation (rad)Tension force (kN) No bolt slip (model) Bolt slip (model) Test results Fig.7. Modelresponsewithandwithoutboltslipinfluencecompared totheexperimentalresultsofathree-boltconnectionbyThompson ( 2009 )ASCE04013041-7J.Struct.Eng.

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controlledbytheedgetear-outcomponent,thepeakvaluesof tensionandsheararemostsensitiveto Ce 1,whereasthepeak momentismostsensitivetotheinitialstiffnessoftheedgetearoutcomponent( Ke 1). Testcase7exhibitsthehighestvariabilityinthepeaktension,as showninFig. 5 .ThescatterplotsinFig. 8 showthesensitivityof thepeaktensionofTestcase7tothevariationin Cb 1, fub, Ce 1,and Ke 1,whicharethetopfourinfluentialvariables.Thevariableson theabscissaarenormalizedsuchthattheoriginrepresentsthemean value,andeachunitrepresents1standarddeviation.Theconnectionhaslowpeaktensionvalueswhenboltshearfailuregoverns, whereasthepeaktensionalmostdoubleswhentheconnectionfails byedgetear-out.Whentheboltshearcapacityparametersarelower thantheirmeanvalues,theconnectionfailspredominantlyinbolt shear.Incontrast,forthesampleswithlowstrengthandstiffness parametersoftheedgetear-outcomponent,thedisplacementdemandsontheboltaregreatlyreduced,andtheconnectionfailure modeswitchestotheplateedgetear-outcomponent.Astheedge tear-outcomponentisductile(i.e.,maintainsthepeakloaduntilthe displacementequals Leh= 2 ),morethanoneboltspringattainsits peakforcebeforetheloadlossbegins,resultinginahighertotal tensionintheconnection.ThisexplainstheunderlyingphenomenonfortheobservedhighvariabilityforTestcase7.Thechange fromabrittletoaductilefailuremodeincreasesthepeakforceon theconnectionconsiderably.Thus,asthedifferencebetween componentspringnominalcapacitiesdecreases,thevariability intheconnectionpeakforceincreases.DiscussionThefailuremodesofthespecimenstestedbyThompson( 2009 ) indicatethattheplatefractureandedgetear-outmodesmayinteract undercatenaryaction.Inparticular,theoutermostbolts(eitherat thetoporbottom)thataresubjectedtothemaximumsheardemand undercombinedrotationandaxialloadingmaydisplayedgetearoutalongtheplatecorneroroneplaneofhorizontaledgetear-out andaverticaltensilesplitting.Thismaycontributetothelarge variabilityobservedintheconnectionpeakforcesforTestcase 7inFig. 5 .Furthermore,becauseTestcases6 – 8weremodeled withoutthetwo-spansubassembly,discrepanciesintheloadingbetweenthemodelandthetestmayexist,astheinteractionbetween thetwosheartabconnectionswithinthetestsetupandtheflexibilityoftheboundaryconditionsareignored.MainandSadek ( 2012 )suggestthatinthepresenceoftwosheartabconnections inatwo-spansubassembly,thedeformationpasttheultimate Table6. EmpiricalFactorDistributionParameters(Datafrom KoduruandDriver2012 ) ModelparameterMeanStandarddeviationDistribution Bolttensiletoshearconversionfactor, Cb 10.620.030Lognormal Areareductionfactorforboltthreadsinshearplane, Cb 20.770.024Lognormal Empiricalfactorforpostyieldstiffnessofbolt, Kb 15.590.587Uniform Empiricalfactorforinitialstiffnessofbolt, Kb 20.400.160Uniform Empiricalfactorforedgetear-outcapacity, Ce 11.050.087Uniform Empiricalfactorforinitialstiffnessofedgetear-outcomponent, Ke 11.920.104Uniform Empiricalfactorforpostyieldstiffnessofedgetear-outcomponent, Ke 20.0110.0009Uniform Empiricalfactorforinitialboltbearingstiffnessinedgetear-outcomponent, Ke 31327.20Uniform Postpeakstiffnessdegradationfactorforedgetear-outcomponent, Cstiff0.750.14Uniform Table7. RankingofInfluentialVariablesonPeakConnectionForces TestcaseaPeakforceparameter Rank 1234 6Tension Cb 1Ce 1fubKe 1Shear Cb 1fubCe 1Ke 1Moment Cb 1fubKe 1Ce 17Tension Cb 1fubCe 1Ke 1Shear Cb 1Ce 1fubKe 1Moment Cb 1fubKe 1Ce 18Tension Cb 1fubCe 1Ke 1Shear Cb 1fubCe 1Ke 1Moment Cb 1fubKe 1Ce 19Tension Cb 1Cb 1fubKe 1Shear Cb 1fubKe 1tpMoment Ke 1Kb 2Ke 3Ce 110Tension Cb 1fubCe 1Ke 1Shear Cb 1fubKe 1CstiffMoment Ke 1Kb 2Ce 1Ke 311Tension Ce 1Ke 1fubCstiffShear Ce 1CstiffKe 1fubMoment Ke 1Ce 1fubtp aThereferenceforeachtestcaseisshowninTable 1 -2 -1 0 1 2 100 200 300 400 500 600 Cb1Tension (kN) -2 -1 0 1 2 100 200 300 400 500 600 fubTension (kN) -2 -1 0 1 2 100 200 300 400 500 600 Ce1Tension (kN) -2 -1 0 1 2 100 200 300 400 500 600 Ke1Tension (kN) Bolt Shear failures Edge Tear-out failures (a) (b) (c) (d) Fig.8. Sensitivityoftensilecapacitytovariation:(a)empiricalfactor forboltshearstrength;(b)bolttensilestrength;(c)empiricalfactorfor edgetear-outcapacity;(d)empiricalfactorforinitialstiffnessofedge tear-outcomponentASCE04013041-8J.Struct.Eng.

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loadmaybelocalizedinoneconnectionandnotsymmetrically distributedbetweenthetwoconnections. Boltsliphadasignificantinfluenceonthebehaviorofthe three-boltconnections.ForTestcase6,Fig. 7 showsthatwithout consideringtheboltslip,themodeloverpredictsthepeaktensile forceby67%.Inclusionoftheboltslipeffectreducesthiserrorto 16%butincreasestheerrorintheoverpredictionofmoment capacityfrom2to26%andincreasestheunderpredictionof therotationatmaximumtensionfrom4to14%.Thisindicates thatthethree-boltconnectionint hetestexhibitsmoreflexibility thanthecomponent-basedmodel.Asdiscussedpreviously,the additionalflexibilitycouldbea ttributedtotheboundaryconditionsandtheinteractionoftheothersheartabconnectioninthe testsetup.Furthermore,alargeec centricitybetweenthecenters ofrotationoftheconnectionsontheeitherendofabeammay causeinitialcompressivearchingaction,asdiscussedby Daneshvaretal.( 2012 ).Thiseccentricitynotonlyresultsin compression,ratherthancatenarytension,ontheconnectionat smallrotationsbutalsointr oducesdiscrepancybetweenthe measuredbeamendrotationand therotationattheboltlineof thesheartabconnectionusedinthemodelvalidation,inaddition tothedifferencescausedbytheboltslip.Incontrast,forTestcase 9,theinclusionoftheboltslipeffectreducedtheerrorinthe predictionofshearcapacity from49to2%andtheerrorin thepredictionoftherotationatfailurefrom24tolessthan 1%.Inthecaseofdeeperconnections,withfourormorebolts, theinitialconnectio nrotationassociatedwiththeboltslipis negligiblebecausetheaxialdef ormationdemandataboltspring increaseswiththenumberofbolts,andtheboltbearingoccursat significantlylowconnectionrotations. Theweldcomponentdidnotfailinanyofthetests.Furthermore,itcontributeslittletotheconnectionductilitybecauseof itshighstiffness.Thefailuremodesattributedtoboltshear(Test cases1,4,5,9,10,andtwospecimenseachofTestcases6and7), platefracture(Testcase3andtwospecimenseachofTestcases 6 – 8),edgetear-out(Testcases2and11),andcombinations (twospecimenseachofTestcases7and8)areprominentinmost ofthetests.Hence,thevariablescorrespondingtothesecomponentshaveresultedinbeingthemostinfluentialontheconnection capacitiesintensionandshear,asshowninTable 7 .Conversely,the momentcapacityissensitivetothevariablesinfluencinginitial stiffnessinadditiontotheultimatefailuremodebecauseatalower stiffnesstheconnectionbecomesmoreefficientinresistingthe loadsbycatenaryaction.ConclusionsAcomponent-basedmodelforpredictingthesheartabconnection performanceunderavarietyofloadcombinationsisvalidated.The proposedmodelusestheavailableresearchontheconnection componentsandprovidesreasonablyaccurateresultsatlowcomputationalcosts.Moreover,itusestheavailablenominaldesignvaluesoftheconnectionparametersandallowsformodelextension withrelativeease.Themodelperformswellinpredictingloadcombinationsattributedtocatenaryactionsandprovidesaninteraction modelforshear-axial-momentloadcombinations.Furthermore, sensitivityanalyseswiththematerial,geometric,andmodelparametersindicatethatthemodelpredictionsforpeakforcesaremore sensitivetowardtheempiricalfactorsofcomponentsthatcontrol theconnectionfailuremode.Furtherresearchisrequiredtoaccount fortheinteractionofplatefracture,boltbearingandedgetear-out failuremodesunderthecatenaryaction,postpeakmodelingof componentspringresponses,andinfluenceofboltsliponthe connectionductility.AcknowledgmentsThefirstauthorgratefullyacknowledgesfundingfromtheNatural SciencesandEngineeringResearchCouncil(NSERC)ofCanada intheformofpostdoctoralfellowship.ReferencesAstaneh,A.,Call,S.M.,andMcMullin,K.M.(1989). “ Designofsingle plateshearconnections. ” Eng.J. ,26(1),21 – 32. Crocker,J.P.(2001). “ Adeformationlimitstateforsingleplateshear connectionssubjectedtoseismicloading. ” Ph.D.dissertation,Univ. ofUtah,SaltLakeCity,UT. Crocker,J.P.,andChambers,J.J.(2004). “ Singleplateshearconnection responsetorotationdemandsimposedbyframesundergoingcycliclateraldisplacements. ” J.Struct.Eng. ,10.1061/(ASCE)0733-9445(2004) 130:6(934),934 – 941 Daneshvar,H.,Oosterhof,S.A.,andDriver,R.G.( 2012). “ Compressive archingandtensilecatenaryactioninsteelshearconnections undercolumnrem ovalscenario. ” Proc.,3rdInt.StructuralSpeciality Conf. ,CanadianSocietyforCivilEngine ering,Montreal,QC,Canada. Dept.ofDefense(DoD).(2009). “ Unifiedfacilitiescriteria.Designof buildingstoresistprogressivecollapse. ” UFC4-023-03 ,Washington, DC. FEMA.(2000). “ Stateoftheartreportonconnectionperformance. ” FEMA-355D ,Washington,DC. GSA.(2003). Progressivecollapseanalysisanddesignguidelinesfor newfederalofficebuildingsandmajormodernizationsprojects Washington,DC. Guravich,S.J.(2002). “ Standardbeamconnectionsincombined shearandtension. ” Ph.D.dissertation,Univ.ofNewBrunswick, Fredericton,NB,Canada. Guravich,S.J.,andDawe,J.L.(2006). “ Simplebeamconnectionsin combinedshearandtension. ” Can.J.Civ.Eng. ,33(4),357 – 372. Kim,H.J.,andYura,J.A.(1999). “ Theeffectofultimate-to-yieldratioon thebearingstrengthofboltedconnections. ” J.Constr.SteelRes. ,49(3), 255 – 269. Koduru,S.D.,andDriver,R.G.(2012). “ Uncertaintymodelingofsheartab connections. ” Proc.,3rdInt.StructuralSpecialityConf. ,Canadian SocietyforCivilEngineering,Montreal,QC,Canada. Lesik,D.F.,andKennedy,D.J.L.(1988). “ Ultimatestrengthofeccentricallyloadedfilletweldedconnections. ” StructuralEngineeringRep. 159 ,Univ.ofAlberta,Edmonton,AB,Canada. Liu,J.,andAstaneh-Asl,A.(2004).“ Momentrotationparametersfor compositesheartabconnections. ” J.Struct.Eng. ,10.1061/(ASCE) 0733-9445(2004)130:9(1371),1371 – 1380 Main,J.A.,andSadek,F.(2012). “ Robustnessofsteelgravityframe systemswithsingle-pl ateshearconnections. ” NISTTechnicalNote 1749 ,NationalInstituteofStandard sandTechnology,Gaithersburg, MD. Moore,A.M.,Rassati,G.A.,andSwanson,J.A.(2008). “ Evaluation ofthecurrentresistancefactorsforhigh-strengthbolts. ” Finalrep. Submittedtoresearchcouncilonstructuralconnections ,CEAS-Civil andEnvironmentalEngineering,Univ.ofCincinnati,Cincinnati,OH. Moze,P.,andBeg,D.(2010). “ Highstrengthsteeltensionspliceswithone ortwobolts. ” J.Constr.SteelRes. ,66(8 – 9),1000 – 1010. Oosterhof,S.A.,andDriver,R.G.(2011). “ Anapproachtotesting theperformanceofsteelconnecti onssubjectedtoextremeloading scenarios. ” Proc.,2ndInt.EngineeringMechanicsandMaterials SpecialityConf. ,CanadianSocietyforCivi lEngineering,Montreal, QC,Canada. Oosterhof,S.A.,andDriver,R.G.(2012). “ Performanceofsteelshear connectionsundercombinedmoment,shearandtension. ” Proc.of StructuresCongress2012:ForgingConnectionsintheWindyCity StructuralEngineeringInstituteofASCE.ASCE04013041-9J.Struct.Eng.

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Rex,C.O.,andEasterling,W.S.(2003). “ Behaviorandmodelingofabolt bearingonasingleplate. ” J.Struct.Eng. ,10.1061/(ASCE)0733-9445 (2003)129:6(792),792 – 800 Sadek,F.,El-Tawil,S.,andLew,H.S.(2008). “ Robustnessofcomposite floorsystemswithshearconnections:Modeling,simulation,andevaluation. ” J.Struct.Eng. ,10.1061/(ASCE)0733-9445(2008)134:11(1717), 1717 – 1725 Sarraj,M.,Burgess,I.W.,Davison,J.B.,andPlank,R.J.(2007). “ Finite elementmodelingofsteelfinplateconnectionsinfire. ” FireSaf.J. 42(6 – 7),408 – 415. Taib,M.,andBurgess,I.W.(2011). “ Acomponent-basedmodelfor fin-plateconnectionsinfire. ” Proc.,ApplicationsofStructuralFire Engineering ,CzechTechnicalUniv.,Prague,CzechRepublic, 225 – 230. Thompson,S.L.(2009). “ Axial,shearandmomentinteractionofsingle plate ‘ sheartab ’ connections. ” M.S.thesis,MilwaukeeSchoolof Engineering,Milwaukee,WI. Weigand,J.M.,Meissner,J.E.,Francisco,T.,Berman,J.W.,Fahnestock, L.A.,andLiu,J.(2012). “ OverviewofAISC/NSFstructuralintegrity researchandpreliminaryresults. ” Proc.,StructuresCongress2012: ForgingConnectionsintheWindyCity ,StructuralEngineeringInstitute ofASCE. Yim,H.C.,andKrauthammer,T.(2012). “ Mechanicalpropertiesof single-plateshearconnectionsundermonotonic,cyclicandblastload. ” Eng.Struct. ,37,24 – 35. Yu,H.,Burgess,I.W.,Davison,J.B.,andPlank,R.J.(2009). “ Experimentalinvestigationofthebehavioroffinplateconnectionsinfire. ” J.Constr.SteelRes. ,65(3),723 – 736.ASCE04013041-10J.Struct.Eng.



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1 ASSESSMENT OF DIRECT SHEAR BEHAVIOR IN NORMAL AND ULTRA HIGH PERFORMANCE CONCRETES By ROBIN E. FRENCH A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 201 4

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2 201 4 Robin E. French

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3 To my fianc and family

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4 ACKNOWLEDGMENTS Foremost, I would like to thank my thesis advisor, Dr. Theodor Krauthammer fo r his guidance, assistance and patience throughout my time at the University of Florida. I would also like to thank my thesis committee member Dr. Serdar Astarlioglu for his assistance. Additionally, I would like to express my gratitude to the Defense Thre at Reduction Agency (DTRA) for their generous support in sponsoring this research and the cooperation and support from the U.S. Army Engineer Research and Development Center who provided all the test specimens. I would also like to thank the Canadian Armed Forces and 1 ESU (1 st Engineer Support Unit) for providing my scholarship to complete my graduate studies at the University of Florida. Finally I would like to thank all of my peers at the Center for Infrastructure Protection and Physical Security (CIPPS ), family and fianc for the help and support they have provided throughout this project.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 15 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 17 Problem Statement ................................ ................................ ................................ 17 Objective and Scope ................................ ................................ ............................... 17 Research Significance ................................ ................................ ............................ 18 2 LITERATURE REVIEW ................................ ................................ .......................... 19 Normal Strength Concrete ................................ ................................ ...................... 19 Compressive Strength and Behavior ................................ ................................ 19 Tensile Strength a nd Behavior ................................ ................................ ......... 19 Ultra High Performance Concrete (UHPC) ................................ ............................. 20 Definition ................................ ................................ ................................ .......... 20 Composition ................................ ................................ ................................ ..... 20 Cement ................................ ................................ ................................ ...... 21 Sand ................................ ................................ ................................ .......... 21 Silica fume ................................ ................................ ................................ 2 1 Superplasticizer ................................ ................................ ......................... 21 Fibers ................................ ................................ ................................ ......... 22 Mixing ................................ ................................ ................................ ............... 22 Curing ................................ ................................ ................................ ............... 22 Mechanical Properties ................................ ................................ ...................... 23 Stress strain relationship ................................ ................................ ........... 23 Rate effects ................................ ................................ ................................ 23 UHPC Manufacturers ................................ ................................ ....................... 24 DUCTAL ................................ ................................ ................................ ... 24 CEMTEC Multiscale ................................ ................................ ......................... 25 COR TUF ................................ ................................ ................................ ... 25 Direct Shear Behavior ................................ ................................ ............................. 26 Direct She ar Push Off Tests ................................ ................................ ............. 26 Hofbeck et al. (1969) and Mattock and Hawkins (1972) ............................ 27 Walraven and Reinhardt (1981) ................................ ................................ 28 Valle and Buyukozturk (1993) ................................ ................................ .... 29 Millard et al. (2010) ................................ ................................ .................... 31

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6 Original and Modified Hawkins Shear Models ................................ .................. 32 Summary ................................ ................................ ................................ ................ 34 3 EXPERIMENTAL INVESTIGATION ................................ ................................ ....... 56 Test Spe cimens ................................ ................................ ................................ ...... 56 Test Equipment and Instrumentation ................................ ................................ ...... 57 Static Testing Equipment ................................ ................................ .................. 57 Static Data Acquisition ................................ ................................ ..................... 58 Keyence H157 Hi Accuracy Laser ................................ ................................ .... 58 Small Drop Hammer ................................ ................................ ......................... 58 Large Drop Hammer ................................ ................................ ......................... 59 Dynamic Data Acquisition ................................ ................................ ................. 59 High Speed Camera ................................ ................................ ......................... 60 Summary ................................ ................................ ................................ ................ 60 4 RESULTS AND DISCUSSION ................................ ................................ ............... 71 Static Testing ................................ ................................ ................................ .......... 71 NC Specimens ................................ ................................ ................................ 71 COR TUF1 (CT1) Specimens ................................ ................................ .......... 72 COR TUF2 (CT2) Specimens ................................ ................................ .......... 72 Comparison of 0% Specimens ................................ ................................ ......... 73 Comparison of 0.8% Specimens ................................ ................................ ...... 73 Comparison of 1.6% Specimens ................................ ................................ ...... 73 Impact Testing ................................ ................................ ................................ ........ 75 NC Specimens ................................ ................................ ................................ 75 COR TUF1 (CT1) Specimens ................................ ................................ .......... 76 COR TUF2 (CT2) Specimens ................................ ................................ .......... 76 Comparison of 0% Specimens ................................ ................................ ......... 77 Comparison of 0.8% Specimens ................................ ................................ ...... 77 Comparison of 1.6% Specimens ................................ ................................ ...... 77 Comparison of Static and Impact and Test Results ................................ ................ 78 5 NUMERICAL MODELING ................................ ................................ ..................... 109 Hawkins Direct Shear Model ................................ ................................ ................. 109 Hawkins Model Compared to Valle and Buyukozturk (1993 ) .......................... 109 Hawkins Model Compared to Hofbeck et al. (1969) ................................ ....... 110 Hawkins Model Compared to NCS Test Results ................................ ............ 110 Modified Direct Shear Model ................................ ................................ ................. 110 Modified NCS Direct Shear Model ................................ ................................ .. 111 CT2S Direct Shear Model ................................ ................................ ............... 113 CT1S Direct Shear Model ................................ ................................ ............... 114 6 CONCLUSIONS AND RECOMMENDATIONS ................................ ..................... 124 Conclusions ................................ ................................ ................................ .......... 124

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7 Recommendations for Future Research ................................ ............................... 125 APPENDIX DETAILED EXPERIMENTA L RESULTS ................................ ........... 127 Static Testing ................................ ................................ ................................ ........ 127 NC 1A 0 S ................................ ................................ ................................ ...... 127 NCS 1 1 S ................................ ................................ ................................ ...... 128 NCS 1 2 S ................................ ................................ ................................ ...... 129 CT1 1A 0 S ................................ ................................ ................................ .... 130 CT1S 1 1 S ................................ ................................ ................................ .... 131 CT1S 1 2 S ................................ ................................ ................................ .... 132 CT2 1A 0 S ................................ ................................ ................................ .... 133 CT2S 1 1 S ................................ ................................ ................................ .... 134 CT2S 1 2 S ................................ ................................ ................................ .... 135 Impact Testing ................................ ................................ ................................ ...... 136 NC 1A 0 D ................................ ................................ ................................ ...... 136 NCS 1 1 D ................................ ................................ ................................ ...... 139 NCS 1 2 D ................................ ................................ ................................ ...... 142 CT1 1A 0 D ................................ ................................ ................................ .... 145 CT1S 1 1 D ................................ ................................ ................................ .... 147 CT1S 1 2 D ................................ ................................ ................................ .... 149 CT2 1A 0 D ................................ ................................ ................................ .... 152 CT2S 1 1 D ................................ ................................ ................................ .... 155 CT2S 1 2 D ................................ ................................ ................................ .... 158 Comparison of Static and Impact Test Results ................................ ..................... 161 NC 1A 0 ................................ ................................ ................................ ......... 161 NCS 1 1 ................................ ................................ ................................ ......... 162 NCS 1 2 ................................ ................................ ................................ ......... 163 CT1 1A 0 ................................ ................................ ................................ ........ 164 CT1S 1 1 ................................ ................................ ................................ ........ 165 CT1S 1 2 ................................ ................................ ................................ ........ 166 CT2 1A 0 ................................ ................................ ................................ ........ 167 CT2S 1 1 ................................ ................................ ................................ ........ 168 CT2S 1 2 ................................ ................................ ................................ ........ 169 LIST OF REFERENCES ................................ ................................ ............................. 170 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 173

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8 LIST OF TABLES Table pa ge 2 1 Quasi static uniaxial c ompressive performance of UHPCC ................................ 35 2 2 Formulation of Ductal ................................ ................................ ........................ 35 2 3 Formulation of CEMTEC multiscale ................................ ................................ .......... 35 2 4 COR TUF mixture composition ................................ ................................ ........... 36 2 5 Summary of COR TUF and CEMTEC mechanical properties ............................ 36 2 6 Test specimen classification by type of c oncrete and shear reinforcement ........ 37 2 7 Result s for NSC specimens ................................ ................................ ................ 37 2 8 Results for HSC specimens ................................ ................................ ................ 38 2 9 Quasi static shear strength. ................................ ................................ ................ 38 3 1 Push off specimen geometry ................................ ................................ .............. 61 3 2 Push off specimen reinforcement and compressive strengths. .......................... 61 3 3 C IPPS small hammer specifications. ................................ ................................ .. 61 4 1 Summary of static test results. ................................ ................................ ............ 79 4 2 Summary of impact test results. ................................ ................................ ......... 80 4 3 Approximate ratio of dynamic to static shear strength for UHPC. ....................... 81 5 1 NSC, CT2 and CT1 Modified Hawkins direct shear models. ............................ 115 5 2 Modified Hawkins model material input properties. ................................ .......... 116 5 3 Comparison of percent difference in peak shear stresses calculated using Hawkin s and Modified Hawkins models. ................................ .......................... 116

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9 LIST OF FIGURES Figure page 2 1 Typical stress strain curves for concrete in compression. ................................ .. 39 2 2 Typical stress strain curve for concrete ................................ .............................. 39 2 3 Crack patterns in reinforced and fiber reinforced concrete elements subjected to tension ................................ ................................ ................................ ............ 40 2 4 UHPC example mix proportion ................................ ................................ ........... 40 2 5 Bekaert Dramix ZP 305 fibers. ................................ ................................ ............ 41 2 6 Mechanical properties of NSC and fiber reinforced UHPC. ................................ 41 2 7 UHPFRC stress crack opening curve ................................ ................................ 42 2 8 Effect of fibers on UHP FRC on compressive stress strain curve ........................ 42 2 9 Impact compression stress strain curve of UHPCC ................................ ............ 43 2 10 Ductal behavior in compress ion and bending ................................ ................... 43 2 11 Direct shear failure of a reinforced concrete slab ................................ ............... 44 2 12 Shear transfer specimens ................................ ................................ ................... 45 2 13 Push off specimen ................................ ................................ .............................. 45 2 14 Typical load slip curves comparing cracked and uncracked specimens ............. 46 2 15 Effect of concrete strength on shear strength in initially cracked specimens ...... 46 2 16 Proposed relationship between peak shear capacity and fy for cracked specimens of vario us concrete strengths ................................ ........................... 47 2 17 Structure of a crack plane ................................ ................................ ................... 47 2 18 Push off specimen geometry ................................ ................................ .............. 48 2 19 Stirrups and additional reinforcement ................................ ................................ 48 2 20 Maximum shear stresses as a function of concrete compressive strengths, cc sy ................................ ..................... 49 2 21 Shear stress .................. 49

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10 2 22 Sof t sleeves around the bar to eliminate dowel action. ................................ ....... 50 2 23 Crack opening for smooth and deformed bars ................................ .................... 50 2 24 Expected additional cracking for shear loading with deformed bars ................... 50 2 25 Valle and Buyukozturk Push off specimen geometry. ................................ ........... 51 2 26 Cracking patterns ................................ ................................ ............................... 51 2 27 LVDT placement to compare shear deformations along the shear plane ........... 52 2 28 Vertical displacement at the top and middle of the shear plane .......................... 52 2 29 Shear specimen dimensions ................................ ................................ ............... 53 2 30 Shear specimens after testing ................................ ................................ ............ 53 2 31 Dynamic increase factor versus peak loading rate for shear tests ...................... 54 2 32 Original and modified shear stress slip relationship for direct shear ................... 55 3 1 Push off specimen geometry ................................ ................................ .............. 62 3 2 Push off specimen steel reinforcement and forms before pouring concrete. ...... 63 3 3 COR TUF1 specimens being prepared. ................................ ............................. 64 3 4 Push off specimens before being removed from forms. ................................ ..... 64 3 5 Specimen with aluminum tabs. ................................ ................................ ........... 65 3 6 Static testing setup ................................ ................................ ............................. 66 3 7 CIPPS Small drop hammer. ................................ ................................ ................ 67 3 8 Large drop hammer. ................................ ................................ ........................... 68 3 9 Adjustable height pneumatic brakes and UHPC testing stand. .......................... 69 3 10 CIP PS data acquisition system. ................................ ................................ .......... 70 4 1 Comparison of shear stress vs. slip curves for static NC specimens. ................. 82 4 2 NC specimens after s tatic testing ................................ ................................ ....... 83 4 3 NC 1.6% specimens after static testing, demonstrating flexural failure in the top of the specimen ................................ ................................ ............................ 84 4 4 Comp arison of shear stress vs. slip curves for static CT1 specimens. ............... 85

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11 4 5 CT1 specimens during and after testing ................................ ............................. 86 4 6 CT1 specimen s after testing. ................................ ................................ .............. 87 4 7 Comparison of shear stress vs. slip curves for CT2 static specimens. ............... 88 4 8 CT2 specimens after testing. ................................ ................................ .............. 89 4 9 CT2 specimens after static testing ................................ ................................ ...... 90 4 10 Comparison of shear stress vs. slip curves for static 0% shear reinforced specime ns. ................................ ................................ ................................ ......... 91 4 11 Comparison of shear stress vs. slip curves for static 0.8% shear reinforced specimens. ................................ ................................ ................................ ......... 92 4 12 Comparison of shear str ess vs. slip curves for static 1.6% shear reinforced specimens. ................................ ................................ ................................ ......... 93 4 13 CT2S 1 2 S 4 with significant flexural cracking. ................................ ................. 94 4 14 N CS 1 2 S 6 shown with alternate static boundary conditions ........................... 95 4 15 Comparison of shear stress vs. slip curves for dynamic NC specimens. ............ 96 4 16 NC specimens after testing dynamic testing ................................ ....................... 97 4 17 NC 1.6% specimens with flexural failure in the top of the member ..................... 98 4 18 Comparison of shear stress vs. slip curves for dynamic CT1 specimens. .......... 99 4 19 CT1 specimens after dynamic testing showing shear plane failure. ................. 100 4 20 CT1 specimens after dynamic testing ................................ ............................... 101 4 21 Comparison of shear stress vs. slip curves for dynamic CT2 specimens. ........ 102 4 22 CT2 specimens after dynamic testing ................................ ............................... 103 4 23 CT2 specimens after dynamic testing ................................ ............................... 104 4 24 Comparison of sh ear stress vs. slip curves for dynamic 0% shear reinforced specimens. ................................ ................................ ................................ ....... 105 4 25 Comparison of shear stress vs. slip curves for dynamic 0.8% shear reinforced specimens. ................................ ................................ ...................... 106 4 26 Comparison of shear stress vs. slip curves for dynamic 1.6% shear reinforced specimens. ................................ ................................ ...................... 107

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12 4 27 Dynamic and static average peak shear stresses. ................................ ........... 108 5 1 Hawkins model compared to Valle and Buyukozturk (1993) results. ................ 117 5 2 Hawkins model compared to Hofbeck et al. (1969) resu lts. .............................. 118 5 3 Hawkins model compared to test results. ................................ ......................... 119 5 4 Modified Hawkins model. ................................ ................................ .................. 120 5 5 Modified Hawkins model compared to test results. ................................ ........... 121 5 6 Modified Hawkins CT2 model comparison to test results. ................................ 122 5 7 Modified Hawkins CT1 model compared to test results. ................................ ... 123 A 1 Comparison of shear stress vs. slip curves for NC 1A 0 S specimens. ............ 127 A 2 Comparison of shear stress vs. slip curves for NCS 1 1 S specimens. ............ 128 A 3 Shear stress vs. slip curve for NCS 1 2 S specimen. ................................ ....... 129 A 4 Comparison of shear stress vs. slip curves for CT1 1A 0 S specimens. .......... 130 A 5 Comparison shear stress vs. slip curves for CT1S 1 1 S specimens. .............. 131 A 6 Comparison of shear stress vs. slip curves for CT1S 1 2 S specimens. .......... 132 A 7 Comparison of shear stress vs. slip curves for CT2 1A 0 S specimen s. .......... 133 A 8 Comparison of shear stress vs. slip curves for CT2S 1 1 S specimens. .......... 134 A 9 Comparison of shear stress vs. slip curves for CT2S 1 2 S specimens. .......... 135 A 10 The slip vs. time comparison for NC 0% specimens. ................................ ........ 136 A 11 The shear stress vs. time compariso n for NC 0% specimens. .......................... 137 A 12 Comparison of shear stress vs. slip curves for NC 1A 0 D specimens. ........... 138 A 13 The slip vs. time com parison for NC 0.8% specimens. ................................ ..... 139 A 14 The shear stress vs. time Comparison for NC 0.8% Specimens. ..................... 140 A 15 Comparison of shear s tress vs. slip curves for NCS 1 1 D specimens. ........... 141 A 16 The slip vs. time comparison for NC 1.8% Specimens. ................................ .... 142 A 17 The Shear Str ess vs. Time Comparison for NC 1.8% Specimens. ................... 143

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13 A 18 Comparison of shear stress vs. slip curves for NCS 1 2 D specimens. ........... 144 A 19 Comparison of slip vs. time for CT1 0% Specimens. ................................ ........ 145 A 20 Comparison of shear stress vs. slip curves for CT1 1A 0 D specimens. .......... 146 A 21 Comparison of shear stress vs. time for CT1 0% specimens ........................... 147 A 22 Comparison of shear stress vs. slip curves for CT1 1 1 D specimens. ............ 148 A 23 Comparison of slip vs. time for CT1 1.6% specimens. ................................ ..... 149 A 24 Comparison of shear stress vs. time for CT1 1.6% specimens. ....................... 150 A 25 Comparison of shear stress vs. slip curves for CT1S 1 2 D specimens. .......... 151 A 26 Comparison of slip vs. time for CT2 0% specimens. ................................ ........ 15 2 A 27 Comparison of shear stress vs. time for CT2 0% specimens. .......................... 153 A 28 Comparison of shear stress vs. slip curves for CT2 1A 0 D specimens. .......... 154 A 29 Comparison of slip vs. time for CT2 0.8% specimens. ................................ ..... 155 A 30 Comparison of shear stress vs. time for CT2 0.8% specimens. ....................... 156 A 31 Comparison of shear stress vs. slip curves for CT2S 1 1 D specimens. .......... 157 A 32 Comparison of slip vs. time for CT2 1.6% specimens. ................................ ..... 158 A 33 Comparison of shear stress vs. time for CT2 1.6% specimens. ....................... 159 A 34 Comparison of shear stress vs. slip curves for CT2S 1 2 D specimens. .......... 160 A 35 Comparison of shear stress vs. slip curves for NC 1A 0 specimens. ............... 161 A 36 Comparison of shear stress vs. slip curves for NCS 1 1 specimens. ............... 162 A 37 Comparison of shear stress vs. slip curves for NCS 1 2 specimens. ............... 163 A 38 Comparison of shear stress vs. slip curves for CT1 1A 0 specimens. .............. 164 A 39 Comparison of shear stress vs. slip curves for CT1S 1 1 specimens. .............. 165 A 40 Compa rison of shear stress vs. slip curves for CT1S 1 2 specimens. .............. 166 A 41 Comparison of shear stress vs. slip curves for CT2 1A 0 specimens. .............. 167 A 42 Comparison of shear stress vs. slip curves for CT2S 1 1 specimens. .............. 168

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14 A 43 Comparison of shear stress vs. slip curves for CT2S 1 2 specimens ............... 169

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15 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ASSESSMENT OF DIRECT SHEAR BEHAVIOR IN NORMAL AND ULTRA HIGH PERFORMANCE CON CRETES By Robin E. French May 2014 Chair: Ted Krauthammer Major: Civil Engineering Direct Shear is a sudden and catastrophic failure type commonly observed in reinforced concrete structures under highly impulsive dynamic loads, that can lead to sudden and catastrophic structural failure. The direct shear behavior of normal strength concrete (NSC) under both static and impact loading conditions is not well defined. Furthermore, new ultra high performance concretes are being developed that have yet to be tested in direct shear UHPC mixes entitled COR TUF have been developed by the U.S. Army Engineer Research Center and Development Center (ERDC). One of the mix es developed contains steel fibers ( COR TUF 1) and the other does not ( COR TUF 2). As w ith any new material, it is important to fully characterize its properties. The purpose of the study presented in this paper was to conduct quasi static and dynamic testing of both NSC and UHPC shear push off specimens with varying reinforcement ratios. Preliminary re sults from testing were compared to the Hawkins shear transfer model to assess its suitability for predicting direct shear behavior of NSC and COR TUF The findings indicated that the model required modifications to adequately represent the behavior of NSC and COR TUF specimens. Consequently, the model was modified with new coefficients for three type s of concrete studied. This report presents

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16 the study, the findings and provide s conclusions as well as recommendations for future research.

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17 CHAPTER 1 INTROD UCTION Problem Statement Direct Shear is a sudden and catastrophic failure type commonly observed in reinforced concrete structures under highly impulsive dynamic loads. It is a sliding type location where the load or geometry is discontinuous. This failure type can severely compromise the integrity of a structure and can result in progressive collapse. Normal strength concrete (NSC) structural members like beams, columns and boxes have been the subject of many experimental and analytical studies. Conversely, there is little to no reported data on ultra high performance (UHPC) behavior w hen subjected to direct shear. It is not known whether UPC behaves similar to NSC or not. Understanding UHP design of structures, particularly critical facilities. Objective and Scope First, a literature review will be conducted to provide a base of knowledge related to UHPC and previous direct sh ear testing that has been conducted. The primary objective of this research is to obtain data to characterize and understand the direct shear behavior of both NSC and UHPC specimens push off specimens After static and impact tests have been completed, dat a will be processed and analyzed. The resulting shear stress versus slip curves will be compared to the curves predicted by the Hawkins shear model. Appropriate changes will be proposed to the Hawkins shear model for both NSC and UHPC cases if required.

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18 R esearch Significance Direct shear is a sudden and brittle failure type. Improved knowledge of this failure mechanism would result better design and assessment approaches to prevent direct shear failures of NSC and UHPC structural members. This experimental study will characterize the direct shear capacity of COR TUF UHPCs This knowledge will be crucial in ensuring safe design and practices for any structural applications using this relatively new material. This is particularly essential for the effective d esign of protective structures that can be susceptible to direct shear failure during blast events. This study will also explore whether the Hawkins direct shear model that was developed in the 1970s can adequately represent the data obtained from the test ing of push off specimens and use the current data to propose modifications for its improvement

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19 CHAPTER 2 LITERATURE REVIEW This literature provides background of material pertinent to this research. First a brief discussion of the behavior of NSC will be presented. Then the definition, composition, products and behavior of UHPC will be discussed. Lastly, previous research conducted relating to direct shear and shear transfer in concrete will be reviewed. Normal Strength Concrete Wight and MacGregor (201 2) define concrete as a composite material composed of aggregate chemically bound together by hydrated Portland cement. Generally the aggregate is graded in size from sand to gravel, with the maximum size for structural applications being in. Compressiv e Strength and B ehavior Concrete is composed of elastic and brittle materials, however when in compression its stress strain curve is non linear and somewhat ductile. This can be can be explained by the formation of micr o cr acks within the concrete that re sult in a redistribution of stress. Concretes with higher compressive strengths exhibit less ductile behavior than those with lower compressive strengths (Wight and MacGregor 2012). This can be seen in Figure 2 1 Note that as the peak concrete strengths i ncre ase, the descending slope becomes steeper. Also, as the concrete strength increases, the strain corresponding to the peak strength decreases. Tensile Strength and B ehavior The tensile strength of concrete typically is between 8 to 15% of the compressiv e strength. This can vary significantly depending on the type of test conducted, the type of

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20 aggregate, and the presence of a compressive stress transverse to the tensile strength (Wight and MacGregor 2012). Concrete in tension has a linear stress strain behavior until first cracking occurs and then drops significantly following a concave parabola until failure. Figure 2 2 shows this behavior. Ultra High Performance Concrete (UHPC) Definition The US Army Engineering Research and Development Center (ERDC) c lassifies UHPC as cementitious materials with unconfined compressive strengths from 138 MPa to 276 MPa (Roth et al. 2008). The Association Franaise de Gnie Civil defined UHPC as a material with a cement matrix and compressive strength in excess of 150 MP a, possibly attaining 250 MPa, and containing steel fibers in order to achieve ductile behavior under tension (Association Franaise de Gnie Civil 2002). Through the addition of steel or polymer fibers, fiber reinforced concretes demonstrate more ductile behavior. These fibers also limit the opening of large cracks and instead develop a dense system of micro cracks Fig ure 2 3 Another improved property of UHPC when compared to NSC, is its high durability. This is attributed to the very low p o rosity as a r esult of its densely packed matrix of constituent materials. Composition The main components of UHPC are cement, sand, silica fume, superplasticizer, water and fibers. Fig ure 2 4 shows a typical proportion of these constituents. Each of these main constit uents will be discussed below. Unlike NSC, there are no coarse aggregates used. As discussed by Richard and Cheyrezy (1995), the elimination of

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21 coarse aggregates enhances the homogeneity of the concrete leading to a denser matrix, and reduction of micro cr acks. Cement Typically, the cement content of UHPCs are two times higher than NSCs (Habel 2004) High compressive strength, ductility and durability of UHPC are attributed to low water to cement ratios. The cement should have a low alkali content, low to m edium fineness and low tricalcium aluminate (C 3 A) content (Richard and Cheyrezy 1995). This reduces water requirements. Sand Quartz sand is typically used as aggregates for UHPCs, due to its high hardness and since it provides good paste aggregate interfac es. Typically the mean particle size is less than 1 mm. The grain size distributions of cement, silica fume and sand need to be optimized to obtain a dense matrix with low permeability (Habel 2004). Silica fume The use of silica fume in UHPCs has three fun ctions. It increases the strength through dense particle packing and its reaction with calcium hydroxide (Habel 2004, Richard and Cheyrezy 1995). The silica fume with its small particle size fills voids in the concrete limiting porosity. Due to the particl es perfect sphericity the fluidity of the mix is improved (Richard and Cheyrezy 1995). Superplasticizer Superplasticizers attach to mineral surfaces and improve the fluidity of the concrete, reducing required water content (Habel 2004). Typical UHPC mixes have a superplastizer content within a range of 0% to 2% (Association Franaise de Gnie Civil 2002).

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22 Fibers Metallic and synthetic fibers are used in concretes to improve ductility Maximum fiber content of a mix is limited by workability issues (Habel 2 004) Rong et al. (2010) investigated the compressive behavior of UHPC with varying percentages of steel fibers. Table 2 1 shows the results for 0%, 3% and 4% fibers by volume. It can be seen that the compressive strength, peak strain and the toughness ind ex increases with the fiber content. The steel fibers used in COR TUF1 are shown in Figure 2 5 The Dramix ZP 305 fibers are approximately 30 mm long and 0.55mm in diameter. The tensile strength is reported to be 1100 MPa (Williams et al. 2009). Mixing Ty pical mixing procedures for UHPC are discussed by Graybeal (2005) and Williams et al. (2009) and are as follows. The dry constituents, cement, sand and silica fume/flour are weighed and dry blended in a mixer for 2 5 minutes. Water and supe rplasitciser are mi xed together and then gradually added to the dry mix. After 5 15 minutes the result is a flowable paste to which the fibers are added and mixed for another 3 10 minutes. Casting is recommended with 20 minutes of mix completion. Curing The curing of UHP C is quite rigorous and varies depending on the manufacturer. COR days. Finally the specimens ar Yang et al. (2009) conducted a study of the effect of aggregate and curing regimes has on UHPFRC mechanical properties. With respect to curing, they found that specimens

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23 cured at 20 degrees C give app roximately 20% lower compressive strength, 10% lower flexural strength and 15% lower fracture energy than specimens cured at 90 degrees C from 1 to 7 days. Mechanical P roperties Stress strain r elationship UHPCs are characterized by their high compressive a nd tensile strengths when compared to NSC. Another notable characteristic is its ductility through the incorporation of fibers. Figure 2 6 shows typical compressive and tensile stress strain curves of UHPC compared to that of NSC. The most notable differen ce is the gradual softening demonstrated of UHPC tensile stress strain curve when compared to the sharp decrease post peak for NSC. The tensile post peak behavior for ultra high performance fiber reinforced concrete (UHPFRC) varies with fiber content, geom etry, orientation and length compared to maximum aggregate size. The effects of fiber amount and orientations were studied by Fehling et al. (2004). Figure 2 7 shows the range of influence that these variables have when UHPC tensile stress is plotted again st the effects of fiber amounts and orientation on compressive stress strain curve for UHPFRC The effects of fiber content and orientation on compressive strength can be seen in Figure 2 8. Rate e ffect s Compressive strain rate studies of UHPC cylinders wi th varying steel fiber contents were conducted by Rong et al (2010). Fiber contents varied from 0 % to 4% steel fibers by volume. Figure 2 9 shows the test results of the three mixes, each at four different strain rates. It is evident that the peak strengt h increases with increased strain

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24 rates, but more notable is the large increase in the post peak softening curve for the mixes with higher fiber contents. Multiple studies have been conducted concerning the flexural strain rate effects on UHPC, but little literature was found that investigated strain rate effects for d irect shear Shear rate effects in UHPFRC were investigated by Millard et al. (2010). Their testing methods and conclusions are discussed later in this paper in the portion that discusses prev ious direct shear push off tests. UHPC Manufacturers Several different proprietary UHPC mixes have been developed. Three different mixes will be discussed in section. The first two are commercially available mixes, Ductal technology, and CEMTEC multiscale which were both developed in France. The third that will be discussed are the COR TUF mixes developed by the U.S. Army that will be the focus of this experimental study. DUCTAL Ductal is a UHPFRC that has been developed by Lafarge, Bouygues and Rhodia. Ductal enables a range of formulations that can be adjusted to produce properties tailored to its application. Through careful selection of materials, a very de n se mix was developed to minimize void spaces. Through the addition of steel and/or organic fi bers depend ant on the selec ted mix, adequate tensile strength and ductility are achieved. Table 2 2 shows a typical Ductal mix. Compressive and flexural curves for Ductal with steel fibers is shown in Figure 2 10 and compared to NSC. The steel fibers were 2% by volume of the mix and were 13 15 mm in length, with an average diameter of 0.2 mm. They had a tensile strength of 2004 ).

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25 CEMTEC Multiscale CEMTEC Multiscale was developed by The Laboratoire C entral des Ponts et Chausses and is a UHPFRC that incorporates three different types of fibers. The fibers used are three different geometries and sizes and are 11% per volume. This high percentage of fibers and variation in size allow the fibers to perfo rm at the micro and macro scale increasing tensile strength, ductility and bearing capacity (Rossi et al. 2005). According to Rossi et al. (2005), the compressive strength of CEMTEC Multiscale is 205 MPa and an ultimate strain of 0.004. The ultimate tensile strain was reported as It was also reported that the average modulus of rupture was approximately double of that of Ductal Table 2 3 show the formulation of CEMTEC Multiscale. COR TUF COR TUF is an UHPC developed b y ERDC using local materials in an effort to reduce the high production costs associated with other UHPCs Two mixes were developed, one with steel fibers (COR TUF1) and one without (COR TUF2). COR TUF1 contains approximate ly 3.6% steel fibers by volume. T he properties of the fibers and curing process specific to COR TUF were covered earlier in this literature review. Table 2 4 shows the composition of COR TUF by weight. COR TUF cylinders tested by Williams et al. (2009) showed unconfined compressive streng ths ranging from 190 to 244 MPa. Table 2 5 shows a summary of COR TUF material properties compared to CEMTEC Multiscale Values for CEMTEC Multiscale that were obtained using the concrete composition that contains 11 % per volume of steel fibers are given in parentheses.

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26 Direct Shear Behavior Direct shear describes a sliding type failure along a well defined plane, where ns due to loading or geometry. Direct shear failure is s udden and catastrophic. This can occur under static or dynamic conditions. A series of dynamic shear tests were conducted by Slawson on reinforced concrete box structures. The roof slabs were subjected to explosive loads; resulting in very high, short dura tion impulsive loads (Slawson 1984). While some slabs failed in flexure, it was noted that several case that the slabs failed along a vertical plane next to the supports. In these cases, direct shear failure occur red when the member did not have time to re act in a flexural mode. If the member does not fail in direct shear, a flexural mode of failure dominates (Slawson 1984). Figure 2 11 shows the results of one of the tests conducted by Slawson ( 198 4), where the roof slab failed in direct shear. It was foun d that for this specimen 23% of bars crossing the shear plane broke, whereas the remainder pulled out of the side walls. Krauthammer et al. (1986) also studied this test data and proposed the uncoupling of the direct shear response from the flexural respon se. Two single degree of freedom systems were used to evaluate the reinforced concrete slabs responses to the impulse loading. One for the flexural response, considering the response of the section located at the center of the slab, and the other used for monitoring the shear response at the supports. Direct Shear Push Off T ests There have been several different experimental investigations involving direct shear and shear transfer. Commonly used push off specimens are shown in Figure 2

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27 12 These specimens are used to study shear interfaces in reinforced concrete to understand the effects various parameter s have on direct shear behavior. The following sections will provide a summary of r esearch significant to this experimental study. Hofbeck et al. (1969) an d Mattock and Hawkins (1972) Thirty eight specimens were tested in which several parameters were investigated to determine t heir effects on shear transfer. T he difference between initially cracked and uncracked specimens was one of these parameters The st udy also investigated the influence of dowel action, stirrup size and spacing the variation of reinforcement angles and concrete strength A typical push off specimen used in the study is shown in Figure 2 13 Typical load slip curves comparing cracked a nd uncracked shear specimens are shown in Figure 2 14 Test results were normalized using f y where is the percentage of steel shear reinforcement crossing the plane and f y is the yield strength of the steel reinforcement The study found that pre existing cracks reduce the ultimate shear transfer strength and increase the slip at all loads In two series of tests, concrete strength was varied in cracked specimens to study the effects of concre te strength on shear transfer. It was concluded that the concrete strength appeared to set an upper limit on the maximum f y value can contribute to t he ultimate shear capacity. Figure 2 15 compares the two test series (4000 psi and 2500 psi concrete) and shows that at higher reinforcement ratios the 2500 psi specimens show a reduced increase in ultimate shear capacity. A proposed relationship between t he ultimate shear capacity and f y for cracked specimens is shown in Figure 2 16

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2 8 With respect to dowel action, the study found that it has a trivial effect in uncracked concrete, but is significant in cracked concrete. Walraven and Reinhardt (1981) Walraven and Rei n hardt conducted an e xperimental study on the transmission of forces across cracks that were subjected to shear displacements. The main area of interest was the study of the shear crack width and aggregate interlock ( Figure 2 17 ). Testing was done on pre cracked shear specimen s. The variables studied were: the type of reinforcement (embedded bars or external restraint), the concrete strength ( 1.9 ksi < f cc < 8.7 ksi), the concrete type (sand gravel concrete, lightweight concrete), the grading of the concrete (continuous, discon tinuous), t he scale of the concrete (D max = 16 and 32 mm) and the initial crack width. Figure 2 18 shows the push off specimen geometry used The geometry of the specimens is similar to those used by Mattock and Hawkins (1972). The shear plane the push off specimens was 46.2in 2 In specimens with embedded bars, closed form stirrups Additional reinforcement was added in the sides and corners to ensure specimens would fail along the shear plane. The reinforcement used is shown in Figure 2 19 The following w ere some of the conclusions that were made based on the research. It was found that bar size had little influence on the behavior of the specimens when the overall reinforcement ratio was kept constant. Variation of the size of the aggregate by increasing the size from 0.6 in to 1.25 in or removing all particles from 0.01 in to 0.04 also had little influence on behavior.

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29 Increasing the shear reinforcement ratio and the concrete compressive strength resulted in increased maximum shear stresses. This relati onship is clearly shown by the maximum shear stress plotted as a function of the concrete compressive strength and the reinforcement ratio ( Figure 2 20 ) The effect of the inclination of the shear reinforcement crossing the plane was studied by varying th e angle from 45 to 135 degrees. It was concluded that the reinforcement increases in efficiency at angles small er than 90 degrees. Figure 2 21 shows this relationship. T o study the role of dowel action for embedded bars crossing a shear plane, dowel action was eliminated by covering the bars with a soft sleeve on for 20mm on either side of the crack ( Figure 2 22 ) This prevented bond stresses from developing under loading, and resulted in a consta n t crack width. For the deformed bars, when the bond stresses develop a reduction in the crack width in the vicinity of the bars was observed. Figure 2 23 compares the crack width formation for smooth and deformed bars. The diagonal cracking that occurs along the shear plane can be explained by these bond stresses t hat develop and the concrete compression strut that forms from the tension in the reinforcing bars. This behavior can be seen in Figure 2 24 Following testing, a theoretical model was developed to predict shear transfer across a cracked plane. Valle and Buyukozturk (1993) In 1993 a study was conducted by Valle and Buyukozturk to study the effects of fibers, fiber typ e and high strength concrete on uncracked push off specimens. Push off

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30 specimens similar to those used in previous studies were tested and ar e shown in Figure 2 25 Table 2 6 summarizes specimens tested, organized by type, fiber and shear reinforcement. Specimen nomenclature for this study is as follows: normal strength concrete (NC), steel fiber reinforced normal strength concrete (SNC), poly propylene fiber reinforced normal strength concrete (PNC), high strength concrete (HC), steel fiber reinforced high strength concrete (SHC), and polypropylene fiber reinforced high strength concrete (PHC) Specimens in which steel stirrups crossed the shea r plane are A summary of testing results can be found in Table 2 7 for NSC and Table 2 8 for HSC. The study found that the addition of fibers to high strength concrete resulted in greater increa ses in shear strength when compared to normal strength concretes. The enhanced performance of fibers in the high strength concrete was attributed to improved bond characteristics between the fiber and the matrix in the high strength concrete. Fibers were f ound to increase the shear deformation and ductility of both normal and high strength specimens. It was found that in specimens reinforced with fibers alone, failure occurred by the formation of several small diagonal cracks crossing the shear plane, that ultimately join e d and formed a crack band along the shear plane. This cracking pattern is shown in Figure 2 26 A ). Both the steel and polypropylene fibers in NSC specimens were found to pull out of the matrix during failure. In HSC specimens, polypropylene fibers also were observed to have pulled out after some deformation in the fibers Some of the steel fibers yielded and failed in the HSC specimens.

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31 For specimens with shear reinforcement, the diagonal cracking was observed at an angle of 50 to 75 degrees with respect to the horizontal direction ( Figure 2 26 B )) This resu lted in the formation of well defined compressive struts resulting in truss action when combined with the tensile forces carried by the steel stirrups. Ultimate failure occurred when the concrete struts failed in compression. Valle and Buyukozturk (1993) also studied how the measured slip varies at different locations on the shear plane. This was accomplished by placing one LVDT (linear variable differential transformer) to measure the she ar slip at the top of the plane and another to measure the shear slip at the middle of the shear plane. Figure 2 27 shows the placement of the LVDTs used to compare the deformations measured at the top and middle of the shear plane. The results can be seen in Figure 2 28 Note that the LVDT placed at the top begins to measure shear slip at much lower stresses then the LVDT placed at the middle. This is a result of the cracks forming at the top and bottom of the shear plane and propagating towards the center with increasing load. Similar peak shear stresses were measured, but the initial slope is significantly different. This demonstrates how measurements can change based on the placement of instruments Millard et al. (2010) Millard et al. (2010) conducted s train rate research on fiber reinfo rced UHPC in both shear and flexure. Both q uasi static and impact s hear testing was conducted on small shear push off specimens. Dimensions are shown in Figure 2 29 Shear testing was conducted on specimens with steel fib er contents ranging from 1.5 to 6.0 percent by volume. Results from quasi static direct shear testing are shown in Table 2 9 It can be seen that the shear capacity of the blocks increased with higher fiber contents. For

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32 these tests, specimens failed as a result of sliding friction action along the plane and all fibers pulled out of the concrete. For dynamic testing, a drop hammer was used apply a load to the top of the specimen, and loading was controlled by multiple layers of fiber board. Shear specimens that were tested dynamically are shown in Figure 2 30 In some cases, the specimens failed completely before reaching a limiting shear slip of 10 mm, while others maintained some residual strength after the 10 mm displacement was reached. At the strain ra tes tested, there was no significant dynamic increase factor observed. Figure 2 31 shows that there is little to no increase across the strain rates tested. Based on this, the authors proposed no strain rate enhancement for fiber reinforced UHPCs for shear punching resistance. Original and Modified Hawkins Shear M odels Mattock and Hawkins (1972) proposed a model for direct shear based on the shear stress slip relationship. The model was developed to empirically describe the shear transfer of reinforced conc rete members with will anchored reinforcement in the static domain without compressive forces. This model was modified by Krauthammer et al. (1986) to account for compression and rate effects produced by dynamic loads. Krauthammer et al. (1986) proposed th at an enhancement factor of 1.4 be used to account for the effects of compression and rate. The original and modified Hawkins shear model can be seen in Figure 2 32 The model s line segments are described below.

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33 Segment OA : The elastic response prior to concrete cracking is defined by the shear resistance for a slip of 0.004 in. The resistance is given by the expression: (2 1) w here both and f` c are in psi. The initial elastic limit should be no greater than Segment AB : The slop of the curve decreases continuously with increasing m is reached at a slip of 0.012 in. is given by: (2 2) where c y ar vt is the ratio of total reinforcement area to the y is the yield strength of the reinforcement crossing the plane. Segment BC: The shear strength remains constant with increasing slip at Point C corre sponds to a slip of 0.024 in. Segment CD: The slope of the curve is negative and constant. It decreases to the limiting shear strength ( ). The slope, in units of psi per in, is defined by the following expression: (2 3 ) The limiting shear capacity L is given by the expression: (2 4)

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34 Where A sb s is the tensile strength of the reinforcement, and A c is the cross sectional area. All reinforcement crossing the shear plane is generally used in place of just the bottom reinforcement, A sb Segment DE: The shear capacity remains constant until failure occurs at a slip of max For well anchored bars, the slip for failure is given by: (2 5) Where, (2 6) and d b is the bar diameter in inches. Summary This chapter presented a brief summary of the materials and previous experimental work relevant to the study. NSC, UHPC and mild steel reinforcement were discussed. Previous reinforced concrete direct shear studies and the Hawkins direct shear model were then summarized.

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35 Table 2 1 Quasi static uniaxial compressiv e performance of UHPCC at 60 d ( Ro ng et al. 2010 ) Number Compressive Strength, MPa Peak Value of Strain, 10 3 Elastic Modulu s, GPa Toughness Index c5 c10 c30 UHPCC(V 0 ) 143 2.817 54.7 2.43 2.43 2.43 UHPCC(V 3 ) 186 3.857 57.3 3.59 5.08 5.57 UHPCC(V 4 ) 204 4.165 57.9 4.57 6.32 7.39 Table 2 2 Formulation of Ductal (Lafarge, n.d.) Formulation (kg/m 3 ) Cement 710 Silica fume 230 Ground quartz 210 Sand 1020 Water 140 Superplasticizer 13 Steel fibers 160 Table 2 3 Formulation of CEMTEC multiscale (kg/m3) (Rossi et al. 2005) Material Amount Cement 1050.1 Silica f ume 268.1 Sand 514.3 Water 180.3 Superplasticizer 44 Steel f ibers 858 Water/ cement 0.201 Water/binder 0.160 Air entrained 20.1

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36 Table 2 4 COR TUF mixture composition (Williams et al. 2009) Material Product Proportion by Weight Cement Lafarge, Class H, Joppa, MO 1.00 Sand US Silica, F55, Ottawa, IL 0.967 Silica flour US Si lica, Sil co Sil 75, Berkeley Springs, WV 0.277 Silica fume Elkem, ES 900 W 0.389 Superplasticizer W.R. Grace, ADVA 170 0.0171 Water (tap) Vicksburg, MS municipal water 0.208 Steel fibers 1 Bekaert, Dramix ZP305 0.31 1 Steel fibers used in COR TUF1 mat erial only. Table 2 5 Summary of COR TUF and CEMTEC mechanical properties (Friedrich et al. 2013) Material property CEMTEC COR TUF1 COR TUF2 Wet density (kg/m 3 ) 2557 2328 Dry density (kg/m 3 ) 2490 2256 Water content (%) 2.73 3.24 GPa) 48 (55) 40.9 37.5 0.21 0.23 0.22 Shear modulus (GPa) 17 (19) 16.7 15.3 Bulk modulus (GPa) 28 (32) 25.2 22.7 Constrained modulus (GPa) 50 (57) 47.4 43.1 Compressive strength (MPa) 168 (205) 237 210 Tensile strength (MPa) 11 (20) 5 .58 8.88 Flexural strength (MPa) (20) 25.0 16.0 Splitting strength (MPa) 25.6 9.8 60 Dynamic tensile strength (MPa) 12.6

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37 Table 2 6 Test specimen classification by type of concrete and shear reinforcement (Valle an d Buyukozturk 1993) Specimen Identification Concrete Type Vol. Fraction Steel Fibers, V sf % Vol. Fraction Polypropylene Fibers, V pf % Steel Stirrup Reinforcing NC NC SNC SNC 1.0% PNC PNC 1.0% NCS NC 1.47% SNCS SNC 1.0% 1.47% PNCS PNC 1.0% 1.47% HC HC SHC SHC 1.0% PHC PHC 1.0% HCS HC 1.47% SHCS SHC 1.0% 1.47% PHCS PHC 1.0% 1.47% Table 2 7 Results for NSC specimens (Valle and Buyukozturk 1993) Specimen c psi Max. Load, P t (lb) % Incr. Avg., NC 1 4500 23,251.8 775.06 11.55 775.06 NC 2 4500 22,323.9 744.13 11.09 744.13 SNC 1 4200 30,303.0 1010.10 15.60 36.00 618.26 SNC 2 4200 29,552.1 985.07 15 .20 593.44 PNC 1 4010 23,651.7 788.39 12.45 9.76 788.39 PNC 2 4010 23,556.6 785.22 12.40 785.22 NCS 1 4950 39,258.9 1308.63 18.60 62.10 823.87 NCS 2 4950 38,203.5 1273.45 18.10 805.58 SNCS 1 3800 36,024.9 1200.83 19.48 68.20 669.46 SNCS 2 3800 34, 397.4 1146..58 18.60 621.99 PNCS 1 4900 38,535.0 1284.50 18.35 62.32 747.60 PNCS 2 4900 38,640.0 1288.00 18.40 755.30

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38 Table 2 8 Results for HSC specimens (Valle and Buyukozturk 1993) Specimen c psi Max. Load, P t lb % Incr. Avg., HC 1 9000 24,843.3 828.11 8.73 827.90 HC 2 9000 26,927.1 897.57 9.16 869.07 SHC 1 11,600 45,493.8 1516.46 14.08 58.58 1151.35 SHC 2 11,600 46,172.4 1539.08 14.29 1129.81 PHC 1 9100 29,763.0 992.10 10.40 17.16 884.30 PHC 2 9100 30,220.8 1007.36 10.56 903.38 HCS 1 9680 52,155.0 1738.50 17.67 112.69 1024.21 HCS 2 9680 60,153.9 2005.13 20.38 1054.71 SHCS 1 10,930 67,557.9 2251.93 21.54 139.68 1259.79 SHCS 2 10,930 66,93 0.9 2231.03 21.34 1323.55 PHCS 1 9020 49,377.0 1645.90 17.33 92.45 1009.57 PHCS 2 9020 48,721.5 1624.05 17.10 1001.67 Table 2 9 Quasi static shear strength (Millard et al. 2010). Fiber content ( % by volume) Shear strength (MPa) Standard error (MPa ) 1.5 2.0 24.6 3.0 6.0 38.3 0.3 6.0 hybrid 38.6 1.1

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39 Figure 2 1 Typical stress strain curves for concrete in compression (Wight and MacGregor 2012) Figure 2 2. Typical stress strain curve for concrete (Hsu et al. 1987 )

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40 Figure 2 3 Crack patterns in reinforced and fiber reinforced concrete elements subjected to tension (Brandt 2008) Figure 2 4 UHPC example mix proportion (Park et al. 2008)

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41 Figure 2 5 Bekaert Dramix ZP 305 fibers (Williams et al. 2009) Figure 2 6 Mechanical properties of NSC and fiber reinforced UHPC (Wu et al. 2009)

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42 Figure 2 7 UHPFRC stress crack opening curve (Fehling et al. 2004). Figure 2 8 Effect of fibers on UHPFRC on compressive stress strain curve (Fehling et al. 2004).

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43 Figure 2 9 Impact compressi on stress strain curve of UHPCC (Rong et al. 2010) Figure 2 10 Ductal behavior in compression (left) and bending (right) (Acker and Behloul 2004)

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44 Figure 2 1 1 Direct shear failure of a reinforced concrete slab (Slaws on 1984).

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45 Figure 2 1 2 Shear transfer specimens: (a) push off (b) pull off (c) modified push off (Mattock and Hawkins 1972) Figure 2 1 3 Push off specimen (Hofbeck et al. 1969).

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46 Figure 2 1 4 Typical load slip curves comparing cracked and uncracked specimens (Hofbeck et al. 1969). Figure 2 1 5 Effect of concrete strength on shear strength in initially cracked specimens (Hofbeck et al. 1969).

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47 Figure 2 1 6 Proposed relationship between peak shear capacity and fy for cracked specimens of various concrete strengths ( Hofbeck et al. 1969 ). Figure 2 1 7 Structure of a crack plane (Walraven and Reinhardt 1981)

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48 Figure 2 1 8 Push off specimen geometry ( mm ) (Walraven and Reinhardt 1981) Figure 2 1 9 Stirrups and additional re inforcement (Walraven and Reinhardt 1981)

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49 Figure 2 20 Maximum shear stresses as a function of concrete compressive strengths, cc sy (Walraven and Reinhardt 1981) Figure 2 2 1 Shear stress (Walraven and Reinhardt 1981)

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50 Figure 2 2 2 Soft sleeves around the bar to eliminate dowel a ction (Walraven and Reinhardt 1981) Figure 2 2 3 Crack opening for smooth and deformed bars (Walraven and Reinhardt 1981) Figure 2 2 4 Expected additional cracking for shear loading with deformed bars (Walraven and Reinhardt 1981)

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51 Figure 2 2 5 Valle and Buyukozturk (1993) Push off specimen geometry. Figure 2 2 6 Cracking patterns for (a) no stirrups crossing the shear plane (b) stirrups crossing the shear plane (Valle and Buyukozturk 1993)

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52 Figure 2 2 7 LVDT placement to compare shear deformations along the shear plane (Valle and Buyukozturk 1993). Figure 2 2 8 Vertical displacement at the top and middle of the shear plane (Valle and Buyukozturk 1993).

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53 Figure 2 2 9 Shear specimen dimensions in mm (Millard et al. 2010) Figure 2 30 Shear specimens after testing (Millard et al. 2010).

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54 Figure 2 31 Dynamic increase factor versus peak loading rate for shear tests (Millard et al. 2010).

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55 Figure 2 3 2 Original and modified shear stress slip relationship for direct shear (Krauthammer et al. 1986)

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56 CHAPTER 3 EXPERIMENTAL INVESTIGATION Experi mental testing was required to determine the direct shear properties of NSC, COR TUF1 and COR TUF2. Quasi Static testing took place in the Structures and Materials Testing Lab, an d dynamic impact tests were performed at the UF East Campus using the CIPPS small and large drop hammers. The data gathered from these experiments was used to calibrate the models investigated post testing. Test Specimens The direct shear behavior of concr ete was investigated using initially uncracked push off specimens. An example of a typical test specimen is shown in Figure 3 1 Steel reinforcement placement was similar t o that used by Valle and Boyukoz turk (1993). The intent was to place adequate end re inforcement so that when the specimens were loaded they would fail across the shear plane. Shear reinforcement was present in several specimens in the form of closed stirrups, wrapped around the longitudinal reinforcement. The shear plane reinforcement for each specimen type is summarized in Table 3 1 Three different concrete types were used in this study normal concrete (SAM 35 Williams et al. 2006 ), COR TUF1 and COR TUF2. Specimens were prepared by t he Geotechnical and Structures Laboratory, ERDC, and t he U.S. Army. Figure 3 2 Figure 3 3 and Figure 3 4 show specimens throughout different stages of preparation. The selection of three different concrete types and reinforcement ratios resulted in nine different specimen types that are summarized in Table 3 2 Aluminum angles were attached to the specimens using JB Weld to provide a reflective surface for the lasers that were utilized to measure displacements during static and impact testing. Figure 3 5 shows the aluminum tabs attached to a specimen.

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57 Specime n n omenclature Specimens were named using the following nomenclature. First the type of concrete is identified as normal strength concrete (NC), COR TUF1 (CT1) or COR TUF2 (CT2). The specimens with steel stirrups reinforcing the shear plane are identified identified as being either 1 or 1A. Subsequently the approximate shear reinforcement ratio is identified as 0, 1 or 2 percent. Then the type of test conducted on the speci men is identified as either static (S) or dynamic (D). Lastly the individual specimen is numbered. For example CT2S 1 2 S 2 is the second statically tested COR TUF2 specimen with approximately 2% shear reinforcement, and is size 1. Test Equipment and Inst rumentation This section will outline the equipment and instrumentation that was used during both static and impact testing. Static Testing Equipm ent Figure 3 6 shows a static specimen ready to be tested. Static testing of the specimens was completed using a Tinius Olsen Super L 400 hydraulic testing machine capable of loading up to 400 kips in compression. Testing was done under various load rates that were adjusted based on the specimen material and shear reinforcement ratio. A 700 kip load cell was attac hed to the crosshead so that load data could be in time with displacement data recorded by the two lasers. Two Keyence H157 Hi Accuracy lasers were mounted in a custom built steel housing for protection, and used to measure the displacement of the aluminum tabs throughout the tests. This data was used to obtain the relative slip between the two sides of the shear plane. The shear specimens were placed directly on the base of the testing machine and a Fabreeka

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58 pad Fabreeka International Inc. (2011) was pla ced between the top of the specimen and the load cell. Static Data Acquisition Two types of data were collected throughout static testing, load and displacement data. Displacement data from the lasers collected from the laser head unit using a NI DAQ 6218. Load data was collected from the National Scale Technologies 700 kip load cell using a NI D AQ 9218. Both sets of data were recorded using a custom made LabView program with a sampling rate of 50 Hz. Keyence H157 Hi Accuracy Laser Two Keyence H157 Hi Accur acy lasers were used to measure the displacements for the static and impact tests. These lasers were mounted in a steel housing with a window made from safety glass to protect the lasers during testing. The lasers were set to a range of 35mm and showed a minimum displacement of 0.001mm. Note the laser settings are listed in metric since was the way it was input in the software. The moving average setting was set to one with a sampling cycle of 392 kHz. The measurements from both lasers were recorded durin g testing and the shear slip was obtained during post processing by taking the difference between the two displacements at any given time. Small Drop Hammer Impact testing for NC 1A 0 D and CT2 1A 0 D specimens was conducted using the small drop hammer at CIPPS, as seen in Figure 3 7 It was found that the small drop hammer could not generate enough energy to adequately fail the specimens with relatively high shear capacity, so the large hammer was utilized all other specimens. During initial testing of CT1 S 1 2 D 1, a 300 kips peak load was generated by a total

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59 drop mass of 750 lbs from a height of 11 ft 6 in. This did not fail the specimen. The small drop hammer specifications can be seen in Table 3 3 Pneumatic brakes were configured to fire to prevent th e striker from hitting the specimens multiple times. A 700 kip load cell with a 10 in diameter striker plate was used to measure the load throughout the duration of impact. Large Drop Hammer The C IPPS large drop hammer shown in Figure 3 8 was used to condu ct testing on most of the shear specimens. The drop hammer configuration that was used for testing was capable of dropping a 5715 lb striker in free fall from a maximum height of approximately 20 ft. The maximum drop height used in this series of testing w as 60 in. Similar to the small hammer, pneumatic brakes were used to prevent the striker from impacting the specimen multiple times, or damaging the lasers. These can be seen in Figure 3 9. The same type of 700 kip load cell was used with 10 in striker pl ate to impact the specimen. A Fabreeka pad was placed on top of all specimens. Dynamic Data Acquisition The same data acquisition system was used for both the small hammer and large hammer tests and can be seen in Figure 3 10. The system consists of a Hi gh Techniques HT600 to capture voltages from generated signals, an OASIS 2000 signal conditioner to condition the raw voltage and supply voltage to the load cell, and a rack computer to monitor and save data. The HT600 contains 64 channels that were read i ndependently. Each channel can hold up to 8 million points of data, which can be read up to a frequency of 2 million points per second. The OASIS 2000 is set up with 10 boards capable of regulating voltages to load cells. It can output 5, 10, and 15 V at g ains of 1 to 1000.

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60 High Speed Camera A Phan tom v5.2 high speed camera was used to record the impact testing of the shear specimens. Footage was recorded at 3100 fps, which was the highest possible frame rate that could capture the required field of view. T he footage was utilized to confirm the failure mode of the specimens. When possible, the footage was also used to calculate the striker impact and rebound velocity. Summary This chapter discussed the research approach and methods used in this study A disc ussion of the experimental approach, equipment and instrumentation was then presented.

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61 Table 3 1. Push off specimen geometry Specimen Size L (in) h (in) d (in) b (in) Gap (in) Shear Plane bd (in 2 ) 1 11.5 25 5.5 10 1 55 1A 11.5 27 5.5 11 1.5 60.5 Ta ble 3 2. Push off specimen reinforcement and compressive strengths. Table 3 3. CIPPS small hammer specifications. Drop Hammer Specifications Rail c art w eight 129.46 lb Adapter pl ates t otal 365.00 lb St riker w eight Varying Drop t ower h eight 195.84 in Minimum d rop h eight 12 in Specimen f` c (ksi) Reinforcement Number of Stirrups Stirrup Size NC 1A 0 4.5 0.0% 0 NA NCS 1 1 4.5 0.8% 4 #3 NCS 1 2 4.5 1.6% 8 #3 CT1 1A 0 29 0.0% 0 N A CT1S 1 1 29 0.8% 4 #3 CT1S 1 2 29 1.6% 8 #3 CT2 1A 0 29 0.0% 0 NA CT2S 1 1 29 0.8% 4 #3 CT2S 1 2 29 1.6% 8 #3

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62 Figure 3 1 Push off specimen geometry TABLE 3 2

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63 Figure 3 2 Push off specimen steel reinforcement ( = 0.8%) and forms before pouring concrete.

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64 Figure 3 3 COR TUF1 specimens being prepared. Figure 3 4 Push off specimens before being removed from forms.

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65 Figure 3 5 Specimen with aluminum tabs.

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66 A B Figure 3 6 Static testing setup A) Front view B) Side view.

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67 Figure 3 7 CIPPS Small drop hammer.

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68 Figure 3 8. Large drop hammer.

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69 Figure 3 9. Adjustable height pneumatic brakes and UHPC testing stand.

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70 Figure 3 10. CIPPS data acquisition system.

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71 CHAPTER 4 RESULTS AND DISCUS SION Static Testing This section provides a summary and a brief discussion of the 26 direct shear specimens that were tested. Table 4 1 shows a summary of the static results. Selected shear stress vs. slip graphs are included. Graphs for all successful tes ts can be found in the appendix NC Specimens Figure 4 1 shows results for three NC specimens with different shear reinforcement ratios. There is not a significant difference between the residual capacity of the 0.8 % and 1.6 % specimens. This suggests that the specimens have reached their maximum f y contribution for residual strength of the specimens for normal concrete. This was observed by Hofbeck et al (1969) in their study of cracked push off specimens. Figure 4 2 A) shows an NC specimen with 0% shear reinforcement after failure and shows the diagonal cracks that formed at each corner and propagated across the shear plane. For specimens with shear reinforcement, when failure on the shear plane occurred, the stirrups rotated and did not fail as seen in Figure 4 2 B). Of the five NCS 1 2 S specim ens tested, only one failed on the shear plane. It was discovered that the reinforcement used in the top and bottom of the specimens was inadequate for these blocks with higher reinforcement ratios. This is discussed in more detail in the comparison of 1.6 % static tests Figure 4 3 A) shows NCS 1 2 S 4, the only specimen that failed on the shear plane as intended. A specimen that failed in the top can tilever is shown in Figure 4 3 B).

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72 COR TUF1 (CT1) Specimens A comparison of shear stress versus slip curves for CT1 specimens is shown in Figure 4 4. Unlike NCS specimens, during testing several steel shear reinforcement bars failed. For specimens with shear stirrups it can clearly be seen when the steel reinforcement failed due to sudden drops in the residual c apacity. Unlike CT2S and NCS specimens, CT1S 1.6 % specimens showed an increase in residual capacity when compared to 0.8 %. This can be attributed to the presence of fibers that keep the concrete cohesive as it begins to fracture. This restricts the post pe ak shear stress to a much smaller section of the rebar then CT2S and NCS specimens Figure 4 5 A ) and B) show a CT1 0% specimen during and after testing. The number and arrangement of steel fibers crossing the shear plane varied between specimens. This coul d account for the peak loads ranging between 207 181 kips for 0% specimens. Typically there were fewer fibers crossing the shear plane at the center of the shear plane then around the exterior. No fibers in CT1 specimens were observed to have failed in s hear. Fibers situated on the shear plane were pulled out of the concrete due to insufficient development length Figure 4 6 A) shows a CT1S 0.8 % specimen after testing that resulted in all steel rei nforcement failing. Figure 4 6 B) shows a 1.6 % specimen wh ere only a portion of the steel reinforcement failed. COR TUF2 (CT2) Specimens Results of three CT2 specimens of varying reinforcement ratios are shown in Figure 4 7 As with NCS specimens, an increase of shear reinforcement resulted in higher peak loads, but had limited effect on the residual strength.

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73 Figure 4 8 A) shows a CT2 0% specimen after failure. Diagonal cracks formed during testing, and failure occurred in the shear plane along the vertical reinforcement. As seen in Figure 4 8 B), when CT2S 0.8 % specimens failed, the steel shear reinforcement rotated over a wide area as opposed to being subjected to a localized shear stress as with CT1S specimens. Similar to NCS 1.6 % specimens, CT2S 1.6 % specimens were prone to failing in the top cantilever as op posed to the shear plane. A specimen that failed in the shear plane can be seen in Figure 4 9 A) while one that failed in the upper cantilever is shown in Figure 4 9 B). Comparison of 0% Specimens The t hree different material types are compared in Figure 4 10. Both CT2 and NC specimens failed in a brittle manner. It is worth noting that the presence of fibers in CT1 when compared to CT2 showed slightly more ductile behavior increased the peak load by approximately 160% and provided a small residual capacity Due to the presence of steel fibers, CT1 0% specimens showed some post peak residual strength. Comparison of 0.8 % Specimens Three typical test results for 0.8 % specimens of varying concrete are compared in Figure 4 11. Once again the addition of fibers m ade a significant increase to shear strength, but not as significant as the case of specimens with 0% shear reinforcement. Comparison of 1.6 % Specimens Figure 4 12 shows a comparison of specimens with 1.6 % shear reinforcement. As previously mentioned, it w as discovered during testing that the specimens with 1.6 % shear reinforcement lacked adequate reinforcement in the top and bottom of the blocks. As a result, the blocks tended to fail at the top of the blocks and not on the shear plane

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74 as intended. In an a ttempt to gain some data from the 1.6 % series of blocks, the blocks were placed a half inch off of center. A portion of the specimens tested in this manner failed on the shear plane. The loading offset introduced changes that have an impact on the data obt ained. First, as a result of the offset a moment was introduced so the failure of the shear plane can no longer be considered as pure shear. This would result in the specimens having a lower peak load then if subjected to pure shear. Second, the moment cau ses a rotation of the top of the block in relation to the base. This became apparent during testing when large cracks developed along the sides of the specimens. Figure 4 13 shows significant cracking that developed during testing due to the half inch offs et. This rotation effects the laser measurements since the lasers are measuring distances in relation to the base. As a result the relative slip calculated based on the difference between the two lasers is greater than the actual slip. This would indicate that the 1.6 % specimens would be stiffer then shown. To investigate whether these top cantilever failures were a result of moments being introduced due to the specimens resting directly on the base of the testing machine, alternate end conditions were used for NCS 1 2 S 6. A large roller was attached to the load cell above the specimen and another roller was welded to a steel plate that rested on the base of the testing machine. Figure 4 14 A) shows the specimen and both rollers during testing. During testi ng, cracking was observed on the top and bottom cantilevers prior to cracking on the shear plane. Then crushing occurred at the base. The combination of cracking and concrete crushing at the base led to the corner portion of concrete breaking (Figure 4 14 B)) prior to a shear plane failure being

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75 achieved. This suggests that upper cantilever failures and base cracking observed in NCS 1 2 S and CT2 1 2 S specimens were due to inadequate end reinforcement and not due to moments being introduced Impact Testin g This section provides a summary and a brief discussion of the 33 direct shear specimens that were tested. More detailed results can be found in the Appendix Table 4 2 shows a summary of the impact testing results. Several drop tests were conducted on th e some specimens to determine the correct drop heights that provided adequate energy to fail the specimen with one impact, but not so much as to overwhelm it. NC Specimens Figure 4 15 shows results for three NC specimens with different shear reinforcement ratios. There were no successful impact tests of the 1.6% specimens. Failure for both occurred in the top of the specimen despite the half inch offset. The 1.6 % specimen has only a slightly higher peak load than 0.8 % specimen Had there been a successful f ailure of the shear plane, it would be expected to be higher. For 0.8 % specimens residual stress can be seen in the plot as a result of the shear stirrups Figure 4 16 A) shows an NC specimen with 0% shear reinforcement after failure and shows the several diagonal cracks that propagated to the edge. Significant flexural cracking can be seen along the right hand edge of the specimen. Like the static results, NCS with 0.8 % reinforcement failed on the shear plane. The stirrups rotated and did n ot fail as seen in Figure 4 16 B). Three NCS 1.6 % specimens were tested, none of which failed on the shear plane, even though the blocks were placed a half i nch off of center. Figure 4 1 7 A) shows a failure in the top cantilever of NC specimen with 1.6 % shear reinforceme nt and

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76 shows flexural cracks that formed at the corner of bottom. Since there are no fibers, spalling occurred during impact l oading. As seen in Figure 4 1 7 B) there are no cracks on the shear plane, only spalling at its top and bottom along with flexural cracks that formed in the top and bottom cantilevers. COR TUF1 (CT1) Specimens Figure 4 1 8 shows results for three CT1 specimens with different shear reinforcement ratios. There is no significant difference of residual capacities between 0.8% reinforcement and 1.6% suggesting that the steel shear reinforcement only e ffects the peak load and does not have a significant effect on the residual capacity. Figure 4 1 9 A) shows a CT1 0% specimen after failure As with the static tests all fibers appeared to pull out. S imilar to CT 1 0% specimens CT1S 0.8% failed in direct shear as seen in Figure 4 1 9 B). N ote all the shear reinforcement bars failed in the same manner as the CT1 0.8% static tests. Figure 4 20 shows CT1 specimens with different shear reinforcement. None failed in an unexpected way among the seven specimens. Similar to the static results, the CT1S 1.6% specimens failed on the shear plane as intended unlike the CT2S and NCS 1.6% specimens COR TUF2 (CT2) Specimens Figure 4 2 1 shows comparison of spe ci mens with diff erent shear reinforcement ratios. As with previous CT1 specimens, higher steel reinforcement results in higher peak load but little effect on residual capacity. A CT2 0% specimen after failure is shown in Figure 4 2 2 A ) Unlike CT1, CT2 speci mens are vulnerab le to a brittle failure due to the absence of steel fibers The p resen ce of steel fibers is attributed to energy distribution which means impact energy

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77 could be transferred to the st ir rups through fibers. As seen in Figure 4 2 2 B ) d ue to t he brittle nature of CT2, the concrete failed allowing the stirrups to rotate instead of failing like the CT1 specimens For 1.6 % specimens, CT2 specimens significant spalling occurred during testing as seen Figure 4 2 3 As previously mentioned, the concre te blocks absorbed most of impact energy during a short time and this resulted in a brittle failure of the concrete instead the shear reinforcement Comparison of 0% Specimens Three typical test results for 0% specimens of varying concrete are compared in Figure 4 2 4 There is not a significant residual capacity from any of three 0% specimens. This means only the stirrups largely contribute to the present of residual shear strength during imp act loading. Comparison of 0.8 % Specimens Figure 4 2 5 shows a com parison of three diffe rent materials with 0.8% shear reinforcement. Unlike 0% specimens, CT1 shows a significantly higher residual strength than the others, which means that the presence of steel fibers increased residual strength. To be specific, impact e nergy from the top of the block could be transferred to the stirrups through steel fibers until the stirrups failed Results of this mechanism are seen in Figure 4 1 9 and Figure 4 20 Furthermore, the steel fibers in CT1 resulted in a higher peak load comp ared to CT2 approximately by 17 0% which is comparable to the static results. Comparison of 1.6 % Specimens The three different material types are compared in Figure 4 2 6 The peak load for CT1 is higher than that of CT2, the increase between them is approx imately 140%

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78 which is less than 0.8 % specimens. Significant r esidual stress occurred only in CT1 testing. As discussed in the static testing section the testing of specimens with half inch offset did not show pure shear strength. Additionally, despite the offset none of the 1.6% NC specimens dynamically tested failed on their shear plane. Similar to the results from static tests, the peak load measured for the 1.6% specimens is less than the actual peak load of the shear plane subjected to pure shear. Comp arison of Static and Impact and Test Results It is a well established fact that most materials exhibit increases in strength as the loading rate or strain rate increases. Table 4 3 shows a summary of average peak shear stresses for dynamic and static tests Given the ratios between when comparing the dynamic and static average peak shear stresses for each specimen type, it would appear that there is a strain rate increase in direct shear for NCS and UHPC. Further study is required at a wider range of strain rates prior to determining an appropriate direct shear dynamic increase factor for each material. Figure 2 2 7 shows the comparison of dynamic and static average peak stresses for successful tests.

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79 Table 4 1. Summary of static test results. Specimen f` c (ksi) Shear Plane (in 2 ) Peak Load (kips) (ksi) Slip at Peak (in) Avg Residual (kips) avg Residual (ksi) Slip at Ultimate Failure (in) NC 1A 0 S 1 1 5 60.5 41.2 0.68 0.018 0.018 NC 1A 0 S 2 1 5 60.5 43.4 0.72 0.029 0.029 NCS 1 1 S 1 3 5 5 5 59.9 1.09 0.054 30.5 0.55 NCS 1 1 S 2 5 55 62.1 1.13 0.057 NCS 1 2 S 1 3 5 55 NCS 1 2 S 2 3 5 55 NCS 1 2 S 3 3 5 55 NCS 1 2 S 4 5 55 71.1 1.29 0.088 28.0 0.51 NCS 1 2 S 5 3 5 55 75.3 1.37 CT1 1A 0 S 1 1,2 29 60.5 187.4 3.1 0. 106 0.106 CT1 1A 0 S 2 1,4 29 60.5 206.7 3.42 0.067 7.5 0.12 0.067 CT1 1A 0 S 3 1 29 60.5 181.0 2.99 0.123 7.1 0.12 0.124 CT1S 1 1 S 1 1,4 29 55 213.8 3.89 0.090 55.5 1.01 0.650 CT1S 1 1 S 2 1,4 29 55 200.1 3.64 0.086 48.4 0.88 0.820 CT1S 1 1 S 3 1 29 55 208.0 3.78 0.093 40.3 0.73 0.560 CT1S 1 2 S 1 29 55 235.5 4.28 0.134 83.2 1.51 0.620 CT1S 1 2 S 2 29 55 222.0 4.04 0.114 97.3 1.77 0.670 CT2 1A 0 S 1 1 29 60.5 70.7 1.17 0.033 0.033 CT2 1A 0 S 2 1 29 60.5 76.2 1.26 CT2S 1 1 S 1 4 29 55 137.0 2.49 0.074 55.4 1.01 CT2S 1 1 S 2 29 55 121.3 2.21 0.050 70.4 1.28 CT2S 1 1 S 3 29 55 155.9 2.83 0.087 64.8 1.18 CT2S 1 2 S 1 3 29 55 152.4 2.77 CT2S 1 2 S 2 29 55 156.0 2.84 0.078 66.9 1.22 CT2S 1 2 S 3 5 29 55 160.2 2.91 79.8 1.45 CT2S 1 2 S 4 2 9 55 167.0 3.04 0.123 83.5 1.52 1 Complete failure of specimen 2 Test stopped early, did not obtain full residual strength 3 Top of block failed instead of intended shear plane 4 Test stopped after initial crack formed throughout shear plan. Testing restart ed to obtain residual strength. 5 Displacement date lost due to detached tab or laser blocked by debris.

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80 Table 4 2. Summary of impact test results. Specimen f` c (ksi) Hammer Mass (lb) Height (in) Shear Plane (in 2 ) Approx Peak Load (Kip) (ksi) Slip at Ultimate Failure (in) Measured Velocity (mm/s) NC 1A 0 D 1 1 5 750 12 60.5 72 1.19 1.5 2427 NC 1A 0 D 2 1 5 750 12 60.5 78 1.29 1.5 2130 NCS 1 1 D 1 5 5715 12 55 93 1.69 1 1974 NCS 1 1 D 2 5 5715 12 55 88 1.60 1 2011 NCS 1 1 D 3 4 5 5715 12 55 86 1.56 1894 NCS 1 2 D 1 3 5 5715 12 55 101 1.84 1 1823 NCS 1 2 D 2 3 5 5715 12 55 95 1.73 1 1728 CT1 1A 0 D 1 29 5715 24 60.5 265 4.38 1.5 2234 CT1 1A 0 D 2 29 5715 18 60.5 252 4.17 1.5 2775 CT1S 1 1 D 1 29 5715 30 55 285 5.18 1 3060 C T1S 1 1 D 2 29 5715 30 55 285 5.18 1 3160 CT1S 1 2 D 1 1 2 29 5715 18 55 74 1.35 CT1S 1 2 D 1 2 2 29 5715 18 55 270 4.91 CT1S 1 2 D 1 3 2 29 750 102 55 0.225 5223 CT1S 1 2 D 1 4 2 29 750 120 55 CT1S 1 2 D 1 5 2 29 750 138 55 CT1S 1 2 D 2 1 29 5715 24 55 320 5.82 0.393 2867 CT1S 1 2 D 2 2 29 5715 24 55 120 2.18 1 2813 CT1S 1 2 D 3 1 29 5715 30 55 300 5.45 0.437 3402 CT1S 1 2 D 3 2 29 5715 24 55 145 2.64 1 2735 CT1S 1 2 D 4 1 29 5715 45 55 297 5.40 0.640 4046 CT1S 1 2 D 4 2 29 5 715 24 55 222 4.04 1 2696 CT1S 1 2 D 5 29 5715 24 55 346 6.30 1 3723 CT2 1A 0 D 1 1 1 29 750 11 60.5 145 2.40 0.113 2164 CT2 1A 0 D 1 2 1 ,4 29 750 18 60.5 2960 CT2 1A 0 D 2 1 29 750 18 60.5 114 1.88 1.5 2513 CT2 1A 0 D 3 1 29 5715 6 60.5 127 2.10 1.5 1675 CT2 1A 0 D 4 1 29 5715 6 60.5 103 1.71 1.5 1675 CT2S 1 1 D 1 29 5715 24 55 189 3.44 1 2770 CT2S 1 1 D 2 29 5715 18 55 154 2.80 1 2454 CT2S 1 1 D 3 29 5715 18 55 160 2.91 1 2457 CT2S 1 2 D 1 29 5715 30 55 208 3.78 1 3249 CT2S 1 2 D 2 29 5715 30 55 202 3.67 1 3149 1 Complete failure of specimen 2 Trial test to make sure set up is OK 3 Top of block failed instead of intended shear plane 4 Displacement dat a lost due to detached tab or laser blocked by debris.

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81 Table 4 3. Approximate ratio of dynamic to static shear strength for UHPC. Specimen Avg. Peak Shear Stress (ksi) Ratio (D/S) Dynamic Static NC 1A 0 0 1.24 0.70 1.77 NC 1 1 0.8 1.62 1.11 1.46 NC 1 2 1.6 1.78 1.33 1.34 CT1 1A 0 0 4.27 3.17 1.35 CT1 1 1 0.8 5.18 3.77 1.37 CT1 1 2 1.6 5.74 4.16 1.38 CT2 1A 0 0 2.13 1.21 1.75 CT2 1 1 0.8 3.05 2.51 1.21 CT2 1 2 1.6 3.73 2.89 1.29

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82 Fi gure 4 1. Comparison of shear stress vs. slip curves for static NC specimens.

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83 A B Figure 4 2. NC specimens after static testing. A) NC 1A 0 S 2 after failure. B) NCS 1 1 S 2 after failure, showing rotated reinforcement.

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84 A B Figure 4 3. NC 1.6 % specimen s after static testing, demonstrating flexural failure in the top of the specimen. A) NCS 1 2 S 4 after shear plane failure. B) NCS 1 2 S 3 after specimen top failed.

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85 Figure 4 4. Comparison of shear stress vs. slip curves for static CT1 specimens.

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86 A B Figure 4 5. CT1 specimens during and after testing. A) CT1 1A 0 S 3 during shear plane failure. B) CT1 1A 0 S 2 after failure.

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87 A B Figure 4 6. CT1 specimens after testing. A) CT1S 1 1 S 3 all shear reinforcement fail ed during shear plane failure. B) CT1S 1 2 S 1 during shear failure.

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88 Figure 4 7. Comparison of shear stress vs. slip curves for CT2 static specimens.

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89 A B Figure 4 8. CT2 specimens after testing. A) CT2 1A 0 S 1 after failure. B) CT2S 1 1 S 3 after failure.

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90 A B Figure 4 9. CT2 specimens after static testing. A) CT2S 1 2 S 4 rotated rebar after failure. B) CT2S 1 2 S 1 top of specimen failed.

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91 Figure 4 10. C omparison of shear stress vs. slip curves for static 0% shear reinforced specimens.

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92 Figure 4 11. Comparison of shear stress vs. slip curves for static 0.8 % shear reinforced specimens.

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93 Figure 4 12. Comparison of shear stress vs. slip curves for stat ic 1.6 % shear reinforced specimens.

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94 Figure 4 13. CT2S 1 2 S 4 with significant flexural cracking.

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95 A B Figure 4 14. NCS 1 2 S 6 shown with alternate static boundary conditions. A) NCS 1 2 S 6 before failure. B) NCS 1 2 S 6 after failure.

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96 Figure 4 1 5 Comparison of shear stress vs. slip curves for dynamic NC specimens.

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97 A B Figure 4 1 6 NC specimens after testing dynamic testing. A) NC 1A 0 D 1 after failure. B) NCS 1 1 D 1 after failure.

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98 A B Figure 4 1 7 NC 1.6 % specimens with flexu ral failure in the top of the member. A) NCS 1 2 D 1 top of specimen failed. B) NCS 1 2 D 2 top of specimen failed.

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99 Figure 4 1 8 Comparison of shear stress vs. slip curves for dynamic CT1 specimens.

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100 A B Figure 4 1 9 CT1 specimens after dynamic test ing showing shear plane failure. A) CT1S 1A 0 D 1. B) CT1S 1 1 D 1

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101 A B Figure 4 20 CT1 specimens after dynamic testing. A) CT1S 1 1 D 2. B) CT1S 1 2 D 2

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102 Figure 4 2 1 Comparison of shear stress vs. slip curves for dynamic CT2 specimens.

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103 A B Figure 4 2 2 CT2 specimens after dynamic testing. A) CT2 1A 0 D 2 B) CT2S 1 1 D 2

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104 A B Figure 4 2 3 CT2 specimens after dynamic testing. A) CT2S 1 2 D 1 B) CT2S 1 2 D 2

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105 Figure 4 2 4 Comparison of shear stress vs. slip curves for dynamic 0% shea r reinforced specimens.

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106 Figure 4 2 5 Comparison of shear stress vs. slip curves for dynamic 0.8% shear reinforced specimens.

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107 Figure 4 2 6 Comparison of shear stress vs. slip curves for dynamic 1. 6 % shear reinforced specimens.

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108 Figure 4 2 7 Dynamic an d static average peak shear stresses. 1.00 2.00 3.00 4.00 5.00 6.00 7.00 0 0.5 1 1.5 2 Shear Stress (ksi) Reinforcement Ratio (%) NC-Dynamic NC-Static CT1-Dynamic CT1-Static CT2-Dynamic CT2-Static

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109 CHAPTER 5 NUMERICAL MODELING This section will first compare the results of previous studies to the Hawkins direct shear model and then to the static results of this study. After the comparison is made, modification s will be made to the model to better replicate test data for each material tested. Hawkins Direct Shear Model As discussed in Chapter 2, the Hawkins (1972) direct shear model was proposed to describe the shear transfer of reinforced concrete members in th e static domain. Prior to applying the Hawkins Shear Model to UHPC, it will be compared to experimental data. Hawkins Model Compared to Valle and Buyukozturk (1993) For the direct shear specimens tested by Valle and Buyukozturk (1993), the Hawkins shear mo del is applied to see its usefulness in capturing the s hear stress shear slip behavior. The comparison of test results and model prediction can be seen in Figure 5 1. The peak shear stress recorded was 1.32 ksi and was predicted by the Hawkins model to be 1.27 ksi. This is a difference of 4%. While the Hawkins model appears to approximate initial stiffness, the post cracking stiffness and peak shear stress quite well, the post peak behavior is quite different. The previous tests were not conducted to obtain residual strength data; however, the post peak slope seems shallow in comparison to test data. The predicted residual shear capacity appears to be high.

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110 Hawkins Model Compared to Hofbeck et al. (1969) In order to compare the Hawkins model to test results with a wider range of reinforcement ratios in normal strength concrete, it will be compared to uncracked push off tests conducted by Hofbeck, et al (1969). While the experimental study did not record any post peak shear stress behavior, it provides peak st ress for a wide range on shear reinforcement ratios. It is evident in Figure 5 2 that when the model is applied to a wide range of shear reinforcement ratios the predicted peak shear stresses begin to diverge at high and low ratios. Hawkins Model Compared to NCS Test Results When the Hawkins predictions are compared to the NCS experimental results from the current study, as seen in Figure 5 3, it is apparent that it does not capture the residual shear capacity. The residual shear capacity of the 1.6 % speci men was predicted to be double that of the 0.8 %, however test results suggest that they are similar. Initial stiffness of the Hawkins model is significantly higher than that observed experimentally. This results in much smaller calculated slips at peak str ess. The maximum shear slip predicted by the model is also well short of experimental data for the 0.8% case Modified Direct Shear Model Based on the above observations, modifications will be made to the Hawkins model to better represent NC test data. Onc e this has been accomplished, it will then be modified to better represent the results for CT1 and CT2 tests. As a result, the model will be tailored to each material.

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111 Modified NCS Direct Shear Model As it has been discussed, the Hawkins model does not ade quately predict peak m L ), and shear slips. After studying the equations and coefficients used in the Hawkins model changes were made to better match the results of this experimental study and those of previous st udies. The equations proposed for use are summarized in Table 5 1. Figure 5 4 shows the proposed Modified Hawkins direct shear model. The maximum shear stress is composed of the contribution of the reinforced concrete on the left and the steel rei nforcement on the ri ght to the peak shear capacity. The calculation of the shear residual capacity was based on the friction generated by the concrete along the slip plane. Friction is dependent upon the normal force, which in this case is generat ed by the rebar that is assumed to be yielding. The vt was limited to account for the fact that residual shear stresses were similar for both 0.8% and 1.6 % specimens. This is in agreement with observations of Hofbeck et al. (1969) and Mattock and Hawkins ( 1972 ) that for a given concrete strength there is a limit to steel reinforcement that provides increased residual shear capacity. The elastic slope (K e ) and the post cracking sl ope (K c ) were chosen to provide slips comparable to those experimentally observ ed. The original Hawkins model utilized 1 2 The use of these two slopes results in slips that are closer to those experimentally observed at the shear reinforcement ratios tested.

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112 It should be noted that when considering unrei nforced concrete sections, only and K e should be utilized. Since there is no shear reinforcement, should not be utilized. It was noted during testing the slip that occurs at a constant peak shear stress varied with the amount of ste el reinforcement. The proposed equation 3 replicates the results and modifies the slip at constant peak shear stress based on the reinforcement ratio. As the reinforcement ratios approach 0%, the slip at constant peak approaches 0. max was limited to the bar diameter of shear reinforcement. The rationale behind this is that by this point either the bars will have failed in shear or rotated past the point where direct shear is still applicable. The input material properties used for t he Modified Hawkins model are shown in Table 5 2. Figure 5 5 show s experimental results compared to the Modified Hawkins model. A comparison numerical comparison of experimental data to the Hawkins and Modified Hawkins models is shown in Table 5 3 The Mod ified Hawkins model adequately predicts peak shear stresses. More test data at various shear reinforcement ratios will be required to ascertain residual shear stresses. The modifications to the initial slopes of the model predict much closer slips to what was observed in this experimental study. When the modified model is applied to NSC tests from Hofbeck et al. (1969) significantly higher slips are predicted than what was observed. As noted by Valle and Buyukozturk (1993) the location at which slips a re m easured on the shear plane e ffect the slips measured. This large discrepancy in slips

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113 could be explained if the slip measured by Hofbeck et al. (1969) was measured at the center of the plane. CT2S Direct Shear Model Modifications were made to the coefficie nts used in the Modified Hawkins model to account for changes in material properties between NSC and UHPC and to better fit experimental results. These changes are summarized in Table 5 1. Modified Hawkins Model predictions for CT2 are compared with test r esults in Figure 5 6. The notable difference between the NC and CT2 models is the use of one pre peak slope as opposed to two different slopes. Contrary to the N C data, for the UHPC data it was hard to distinguish a distinct change in slope where cracking occurs. It was for this reason that only one pre peak slope was used. Aside from this, the same equations were used as the NSC M odified Hawkins model, but coefficients were used to account for increase in peak and residual shear stresses. The high increase in the shear residual capacity could be explained by the CT2 having a higher friction coefficient. This could be explained by the increased toughness of CT2 due to its dense matrix making it less likely for the concrete to break into rubble like the NSC s pecimens. The rubble would reduce the friction along the shear plane. There was a significant increase in the residual shear capacity of the CT2 specimens when compared to the NC specimens of the same reinforcement ratios. A significantly higher friction c oefficient of 2.5 was used for the CT2 model. This could be explained by the dense CT2 matrix being harder to reduce into rubble like the NSC specimens that would reduce friction on the slip plane.

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114 vt was limited the same wa y as the NSC model. More testing will be required to accurately determine which shear ratio should be limited when predicting shear stress residual strength of a push off specimen. CT1S Direct Shear Model The CT1 model was based on the CT2 Modified Hawkins model and some modifications were made to account for changes in behavior and are summarized in Table 5 1 A comparison of test data and model predictions is shown in Figure 5 7. First, to account for a significant increase in peak shear stress 0.9f` t was added. This accounts for addition of steel fibers that are crossing the shear plane. The next modification was the reduction in the coefficient used for the residual shear stress to better fit test results. This could be explaine d by the fact that at this point the fibers have begun to pull out across the shear plane and do not provide much additional capacity. They do however get bent over and act as skids along the shear plane reducing friction between the two concrete surfaces. Un like NSC and CT2 specimens, there was a notable increase in residual shear capacity between 0.8% and 1.6% specimens. It is for this reason that vt was no t limited. More tests at higher shear reinforcement ratios will be required for CT1 to determine what limit would be appropriate. The slip at which the peak shear stress remains constant was noted to be significantly larger than that of both NSC and CT2. Consequently the coefficient 3 was adjusted from 0.012 to 0.033. This change could be explained by the presence of steel fibers crossing the shear plane.

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115 Table 5 1. NSC, CT2 and CT1 Modified Hawkins direct shear mod els. Original Hawkins NSC CT2 CT1 1 K e NA NA K c K u 1 0.004 2 0.012 3 0.024 4 max Units are psi in and psi/in 1 The value for should not be ta ken larger then

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116 Table 5 2. Modified Hawkins model material input properties. Material f` c (psi) f` t (psi) NSC 45 00 CT2 29000 CT1 29000 1300 Table 5 3 Comparison of percent difference in peak shear stresses calculated using Hawkins and Modified Hawkins models. Specimen Peak Shear Stress % Difference Hawkins Peak Shear Stress % Difference Modified Hawkins 1.1B 20.4 1.5 1.2B 15.1 2.0 1.3B 5.6 0.5 1.4B 8.3 6.7 1.5B 1.1 2.6 1.6B 6.7 2.7 Valle NCS 4.1 1.4 NCS 1 1 S 20.7 8.2 NCS 1 2 S 1.1 1.8

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117 Figure 5 1. Hawkins model compared to Valle and Buyukozturk (1993) results.

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118 Figure 5 2. Hawkins model compared to Hofbeck et al. (1969) results.

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119 Figure 5 3. Hawkins model compared to test results.

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120 Figure 5 4. Modified Hawkin s model.

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121 Figure 5 5. Modified Hawkins model compared to test results.

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122 F igure 5 6. Modified Hawkins CT2 model comparison to test results.

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123 Figure 5 7. Modified Hawkins CT1 model compared to test results.

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124 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS Con clusions The direct comparison of CT2 to CT1 shows that the addition of fibers to this UHPC greatly enhances its direct shear capacity in both the peak shear stress and associated slips. Also, the addition of steel fibers increases residual capacity of CT1 from 0.8% to 1.6%. Whereas the residual capacity of CT2 remained the same for both of these reinforcement ratios suggesting it had reached its maximum f y contribution at approximately 0.8%. Within the reinforcement ratios tested, there is no indication t hat CT1 had reached its maximum f y contribution by 1.6%. When comparing the quasi static results to the impact results, it appears that there is an increase in peak shear stress with increasing strain rates. Before a value can be assigned to a dynamic inc rease factor for these materials in direct shear, more testing is recommended at a wider range of strain rates. The Modified Hawkins shear model fairly accurately predicts direct shear behavior of NSC and UHPC push off specimens. The modified model provide s better results than the original model over a wider range of experimental direct shear tests. Further direct shear testing will be required to develop models for UHPCs other than COR TUF The Modified Hawkins shear model is recommended to be used for des ign until a further refined model is developed. The importance of consistent measurement of shear slip should be discussed. All measurements for this study were taking near the top of the shear plane. As such, the Modified Hawkins model is calibrated to pr edict slips at that reference point. As noted by

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125 Valle and Buyukozturk (1993), had measurements been taken near the center of the shear plane, the peak shear stresses the same however the slips would be offset. Recommendations for Future Research Another series of direct shear tests should also be conducted using a commercially produced UHPC to see how t he models developed for COR TUF compare. A wider range of shear reinforcement ratios will be required. Varying sizes of shear reinforcement bars an d shear plane should be also used to investigate their effects on direct shear behavior. This could also help define the reinforcement ratios at which the residual or cracked section strengths are governed by concrete strength. This is especially important investigated in this study. Test data from a wider range of reinforcement ratios would also assist in refining the coefficients used to calculate and the slip at constant pe ak shear stress. Future studies should also be conducted using a wider variation of strain rates to investig ate the effects of rate effect on these materials. Testing should be conducted with UHPC specimens containing a variety of steel fiber contents. Thi s could be used to improve the Modified Hawkins model to incorporate the fiber content into a single UHPC model. This series of testing highlighted the importance of proper corner and side reinforcement details in test specimens. Future test specimens shou ld follow a design similar to Hofbeck et al. (1969) as opposed to that of Valle and Boyukozturk (1993). This will prevent the problems that arose at higher shear reinforcement ratios when specimens failed in top cantilever as instead of the shear plane. Mo re experimental data

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126 would also be beneficial for post peak and residual shear stress modeling as most past experimental data captured peak shear stress. Finite Element Models should be developed that adequately predict NSC and UHPC response when subjecte d to direct shear loading These recommendations, if implement ed will improve available tools to accurately predict the direct shear response of push off specimens, and can build upon the base of knowledge for the direct shear behavior of NSC and UHPC.

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127 A PPENDIX DETAILED EXPERIMENTA L RESULTS Static Testing NC 1A 0 S Figure A 1. Comparison of shear stress vs. slip curves for NC 1A 0 S specimens.

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128 NCS 1 1 S Figure A 2. Comparison of shear stress vs. slip curves for NCS 1 1 S specimens.

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129 NCS 1 2 S Figur e A 3. Shear stress vs slip curve for NCS 1 2 S specimen.

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130 CT1 1A 0 S Figure A 4 Comparison of shear stress vs. slip curves for CT1 1A 0 S specimens.

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131 CT1S 1 1 S Figure A 5 Comparison shear stress vs. slip curves for CT1S 1 1 S specimens.

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132 CT1S 1 2 S Figure A 6 Comparison of shear stress vs. slip curves for CT1S 1 2 S specimens.

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133 CT2 1A 0 S Figure A 7. Comparison of shear stress vs. slip curves for CT2 1A 0 S specimens.

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134 CT2S 1 1 S Figure A 8 Comparison of shear stress vs. slip curves for CT2S 1 1 S specimens.

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135 CT2S 1 2 S Figure A 9 Comparison of shear stress vs. slip curves for CT2S 1 2 S specimens.

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136 Impact Testing NC 1A 0 D Figure A 10. The slip vs. time comparison for NC 0% specimens

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13 7 Figure A 11. The shear stress vs. time comparison fo r NC 0% specimens

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138 Figure A 12 Comparison of shear stress vs. slip curves for NC 1A 0 D specimens.

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139 NCS 1 1 D Figure A 13 The slip vs. time comparison for NC 0.8 % specimens

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140 Figure A 14. The shear stress vs. time Comparison for NC 0.8 % Specimens

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141 Figure A 15 Comparison of shear stress vs. slip curves for NCS 1 1 D specimens.

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142 NCS 1 2 D Figure A 16 The slip vs. time comparison for NC 1.8 % Specimens

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143 Figure A 17 The Shear Stress vs Time Comparison for NC 1.8 % Specimens

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144 Figure A 18 Co mparison of shear stress vs. slip curves for NCS 1 2 D specimens.

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145 CT1 1A 0 D Figure A 19 Comparison of slip vs. time for CT1 0% Specimens

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146 Figure A 20 Comparison of shear stress vs. slip curves for CT1 1A 0 D specimens.

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147 CT1S 1 1 D Figure A 21. C omparison of shear stress vs. time for CT1 0% specimens

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148 Figure A 22. Comparison of shear stress vs. slip curves for CT1 1 1 D specimens.

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149 CT1S 1 2 D Figure A 23. Comparison of slip vs. time for CT1 1.6 % specimens

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150 Figure A 24 Comparison of shear st ress vs. time for CT1 1.6 % specimens

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151 Figure A 25 Comparison of shear stress vs. slip curves for CT1S 1 2 D specimens.

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152 CT2 1A 0 D Figure A 26 Comparison of slip vs. time for CT2 0% specimens

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153 Figure A 27. Comparison of shear stress vs. time for C T2 0% specimens

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154 Figure A 28 Comparison of shear stress vs. slip curves for CT2 1A 0 D specimens.

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155 CT2S 1 1 D Figure A 29 Comparison of slip vs. time for CT2 0.8 % specimens

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156 Figure A 30. Comparison of shear stress vs. time for CT2 0.8 % specimens

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157 Figure A 31 Comparison of shear stress vs. slip curves for CT2S 1 1 D specimens.

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158 CT2S 1 2 D Figure A 32. Comparison of slip vs. time for CT2 1.6 % specimens

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159 Figure A 33. Comparison of shear stress vs. time for CT2 1.6 % specimens

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160 Figure A 3 4 Comparison of shear stress vs. slip curves for CT2S 1 2 D specimens.

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161 Comparison of Static and Impact Test Results NC 1A 0 Figure A 35 Comparison of shear stress vs. slip curves for NC 1A 0 specimens.

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162 NCS 1 1 Figure A 36 Comparison of shear stress vs. slip curves for NCS 1 1 specimens.

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163 NCS 1 2 Figure A 37 Comparison of shear stress vs. slip curves for NCS 1 2 specimens.

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164 CT1 1A 0 Figure A 38. Comparison of shear stress vs. slip curves for CT1 1A 0 specimens.

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165 CT1S 1 1 Figure A 39 Comparison of shear stress vs. slip curves for CT1S 1 1 specimens.

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166 CT1S 1 2 Figure A 40 Comparison of shear stress vs. slip curves for CT1S 1 2 specimens.

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167 CT2 1A 0 Figure A 41 Comparison of shear stress vs. slip curves for CT2 1A 0 specimens.

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168 CT2S 1 1 Figu re A 42 Comparison of shear stress vs. slip curves for CT2S 1 1 specimens.

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169 CT2S 1 2 Figure A 43 Comparison of shear stress vs. slip curves for CT2S 1 2 specimens

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170 LIST OF REFERENCES Acker, P., and Behloul, M. (2004). DUCTAL t echnology: A l arge s pec trum of p roperties, a w ide r ange of a pplications Proceedings of the International Symposium on Ultra High Performance Concrete Kassel University Press, Kassel, Germ any, 11 24. Association Franaise de Gnie Civil. (A u ltra hautes p erformances (BFUP) r ecommandations provisoires (Ultra h igh p erformance f ibre r einforced c oncretes i nter im r France 98. based (FRC) composites after over 40 Composite Structures 86(1 3), 3 9. a < http://www.fabreeka.com/documents/file/products/Fabreeka_Pad.pdf > (Feb. 26, 2014) Fehling, E., Leutbecher, T., and Bunje, K. (2004). Design relevant properties of h ardened Ultra High Performance Concrete Kassel, Germany, 327 338. Friedrich, N., Krauthammer, T., Astarlioglu, S., and Bui, L. (2013). Static and impact testing of normal strength and ultra high performance concrete cylinders Gainesville, Florida. Grayb Characterization of the beha vior of ultra high performance concrete. Ultra high performance fibre reinforced concretes (UHPFRC) and reinforced concrete. Ecole Polytechnique Federale de Lausann e. Hawkins, N. M. (197 4 s trength of stud shear connectors Civil Engineering Transactions, Institute of Engineers 39 45 t ransfer in r einforced c ACI Journal 66(13), 119 128. s he ar t ransfer strength in r einforced c ACI Structural Journal 84(2), 149 160. Shallow buried RC box type structures. Journal of Structural Engineering 110(3), 637 651. Krauthammer, T., Bazeos, N., and Holmquist, T. J. (19 a nalysis of RC box t ype s Journal of Structural Engineering 112(4), 726 744.

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171 http://www.lafarge na.com/wps/portal/lna/products/ductal >. Shear transfer in reinforced concrete recent research. PCI Journal 1(April), 55 75. enhancement of blast resistant ultra high performance fibre reinforced concrete under flexural and shea International Journal of Impact Engineering Elsevier Ltd, 37(4), 405 413. i ngredients of the c ompressive s trength of UHPC as a f undamental s tudy to o ptimize the m ix ing p 112 Park, R., and Paulay, T. (1975). Reinforced Concrete Structures Wiley Interscience, 319 325. r eactive p owder c Cement and Co ncrete Research 25(7), 1501 1511. high International Journal of Impact Engineering Elsevier Ltd, 37(5), 515 520. Rossi, P., Arca, A., Pa Cement and Concrete Research 35(1), 27 33. Roth, M. J., Boone, N. R., Kinnebrew, P. G., Davis, J. L., and Rushing, T. S. (2008). E merging and adaptive threats Vicksburg, MS. Slawson, T. R. (1984). Dynamic s hear f ailure of s hallow b uried f lat r oofed r einforced c oncrete s tructures s ubjected t o b last l oading Vicksburg, MS. Valle, M., and Buyukozturk, O f iber r einforced h igh s trength c oncrete under d irect s ACI Materials Journal 90(2), 122 133. e xperiments on the m echanical b ehaviour of c racks in p lain and r einforced c oncrete s ubjected to s hear l Heron 26(1A). Wight, J. K. (2005). Reinforced c oncrete: m echanics and d esign 5th Ed Pearson Prentice Hall. Williams, E., Akers, S. A., and Reed, P. A. (2006). Laboratory c haracterization of SAM 35 c oncrete g eotec hnical and s tructures Vicksburg, MS.

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172 Williams, E. M., Graham, S. S., Reed, P. A., and Rushing, T. S. (2009). Laboratory c haracterization of Cor TUF c oncrete w ith and w ithout s teel f ibers Vicksburg, MS. Wu, C., Oehlers, D. J., Rebentrost, M., Leach, J., a testing of ultra high performance fibre and FRP Engineering Structures Elsevier Ltd, 31(9), 2060 2069. Yang, S. L., Millard, S. G., Soutsos, M. N., Barnett, S. J., and Le, T. T. (2009). uence of aggregate and curing regime on the mechanical properties of ultra Construction and Building Materials Elsevier Ltd, 23(6), 2291 2298.

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173 BIOGRAPHICAL SKETCH Robin French was born in 1985 in B uckingham, Quebec, Canada. In 2003, he joined the Canadian Army and attended the Royal Military College of Canada graduating in 2008 with a Bachelor of Civil Engineering. After being employed as an Engineering Officer at a Combat Engineer Regiment that inc lud ed a deployment to Afghanistan in 2010, he was awarded a postgraduate scholarship from the Canadian Florida, with a specialization in protective structures. Upon completi on of his degree, Robin was assigned to the 1 st Engineering Support Unit in Kingston, Ontario, Canada.